Solving quadratics by factoring worksheet. Solve quadratic equations by inspection (e.

Solving quadratics by factoring worksheet term and an . Worksheet by Kuta Software LLC Solving Quadratics using factoring & quadratic formula Name_____ ID: 1 ©u Z2X0Q1p7M UKeuHtTaf lSOoXfCtkwna\rJea ZLKLgCl. Factoring Quadratics Worksheets Tags: 10th Grade 8th Grade 9th Grade Master factoring quadratic equations with our worksheets for 8th to 10th graders, designed to boost your math This worksheet features 10 different quadratic equations for students to solve. 6)(x + (x 4. College Algebra Start typing, then use the up and down arrows to select an option from the list. Solve each equation by factoring. com. ) 2x2 =24x− 70 Solve the Quadratic Equations by Factoring Solving quadratics by factorising. Worksheet with 12 problems where students must solve a quadratic by factoring. quadratic equation: an equation that can be written in the form: ax2 + hr + c = Where a,b and c are Our 46 solve quadratics by factoring worksheet is the perfect addition to your teaching arsenal. Solving Quadratic Equations by Graphing A quadratic equation in one variable is an equation that can be written in the Factoring Worksheets Tags: 10th Grade 11th Grade 12th Grade 5th Grade 6th Grade 7th Grade 8th Grade 9th Grade Simplify algebraic factoring with our worksheets for 5th to 12th graders. U H vAflplm `rhipgDhWt\sT Hrle^sbenrhvjeodf. 1. Rated 5 out of 5, based on 2 reviews. The worksheet does not specify that Name: _____Math Worksheets Date: _____ So Much More Online! Please visit: EffortlessMath. Homework: Finish the Note Sheet # (1-13). Number of problems 5 problems. Question 3: A quadratic expression, 2x² − x + c , can be Do you or your students need some extra practice with solving quadratic equations using the Quadratic Formula? If so, this page shares a free collection of printable Quadratic Formula Solving Quadratic Equation Worksheets. Solve the quadratics and reveal the anagram of a film - each quadratic gives 2 answers unless there is an odd number of letters in a word when the answer counts just once. Choose from 11 worksheets of increasing difficulty and get answers, help and video support. I intentionally do not make answers to the printable puzzles and math activities I share on my blog available online because I strive to provide learning experiences for my students that are non-google Solving Quadratic Equations By Factoring Date_____ Period____ Solve each equation by factoring. 5. com ©R n220s1z2u GKBustsab LShoCf8t3wja8rSeZ hLOLCC7. , for x^2 = 49. Challenge them to solve quadratic equations by applying methods such as Factoring Techniques: Factoring is a crucial skill for solving quadratic equations but can be difficult for students to master. Preview. We also solved applied problems using quadratics. &Solve € 2x3=5x2+3x& 6 1-20-17: We began to solve quadratic equations using factoring techniques. When solving linear equations such as 2x − 5 = 21 we can solve for the variable Learning Target #2: Solving by Factoring Methods • Solve a quadratic equation by factoring a GCF. solve by factoring 4x −12x+9=0 4. Name (V10T9h Date Period I 3 4) (2m + + 3) = O Solve quadratic equations by inspection (e. 3. How to Solve Quadratic Equations using Factoring Method This is the easiest method of solving a quadratic equation as long as the binomial or trinomial is easily factorable. This worksheet reminds students of the methods involved in factorizing and solving quadratic equations. Solving Quadratic Equations by Factoring Worksheet 1 Answers Solve each equation by factoring. This product tackles this challenge head-on by providing a comprehensive set of worksheets that cover all aspects of factoring and its Factoring Polynomials in Quadratic Form Examples: Worksheet by Kuta Software LLC Practice 7. about. Puzzle Solutions. ) x2 = 3x 3. KG. 1) k + 1)(k − 5) P m 7A 0lVl3 QrmiDgnhet usn nr0eXsXeirSv 0egdy. Word Problems on Quadratic Equations by Solving Quadratics By Factoring Worksheet Answer Key With Work – Quadratic equations can be solved with this Quadratic Worksheet. solve by factoring 2x +x−6=0 2. Up to this point, we have solved linear equations, which are of Factoring Quadratics Worksheets - Grab our free math worksheets featuring exercises in mathematics to ace the problem-solving methods of different mathematical topics. Factoring and Solving Quadratic Equations Worksheet Math Tutorial Lab Special Topic Example Problems Factor completely. x2 144 6. 1 Determine whether a relationship is a function and identify Quadratics - Complete the Square Objective: Solve quadratic equations by completing the square. factor: terms or expressions that when multiplied form a product. Learning how to solve equations is one of our main goals in algebra. 𝑥2−2𝑥−15=0 (𝑥+3)(𝑥−5)=0 𝑥=−3,5 5. ) x2 =4x+ 32 2. 4 Factor completely by factoring out a GCF, then factoring the remaining trinomial. When solving quadratic equations in the past we have used factoring to solve for our variable. To solve word problems involving quadratic equations, you will need to know how to either factor the quadratic equation and set it equal to zero or else Solve the Quadratic Equations Name:_____ by Factoring http://math. Each of these quadratics can be solved by factoring. When you solve the following general equation: $$\red 0 = ax^2 + bx + c Solve Quadratic Equations by Factoring; Solve Quadratic Equations by Completing the Square; Quadratic Formula Worksheets. • Solve a quadratic equation by factoring when a is not 1. Solve a quadratic equation by factoring when a is not 1. Factor completely. The quadratic equations worksheets on this page will require students to solve quadratic equation problems using five different methods including completing the square, factoring, finding the roots, 1. _____ b. Printable in convenient PDF format. This math worksheet Notebook Groups Cheat Sheets Worksheets Study Guides Practice Verify Solution. Solving quadratic equations w/ square roots; Solving quadratic equations by factoring; Solving Quadratic Equations by Factoring. Quadratics*Worksheet* * Factoring* 1. This worksheet will teach you how to solve quadratic problems Free Algebra 2 worksheets created with Infinite Algebra 2. Number of Solve By Factoring Quadratics Worksheet – This Quadratic Worksheet will help you with quadratic equations. Solving Quadratics Week of April 6. com Solve a Quadratic Equation by Factoring Solve each equation by Solving Quadratics: Factorising 1 Video 266 on www. 1) (2r - Kuta Software - Infinite Algebra 1 Name_ Solving Quadratic Equations by Factoring Date_ Period_ Solve Log in Join. Solving quadratics by factoring worksheet LiveWorksheets Liveworksheets transforms your Solve each equation by factoring. A quadratic equation can have one, two, or no zeros. O Y aMXa7dtei LwRi8tdh0 Solve the Quadratic Equations by Factoring Worksheet # 4 1. Solving Quadratic Liveworksheets This polynomials worksheet will produce problems for factoring quadratic expressions. The front side of the worksheet (questions 1-10) include factoring trinomials where a Quadratic Equations Factoring Factoring: Non-Monic 1. Factoring by Solve quadratic equations algebraically. Solve quadratic equations by inspection (e. In grade 10 academic mathematics, students learn about solving quadratic equations by factoring as Solving quadratics mixed problems. 1) x2 - 8x + 16 = 02) 2n2 - 18n + 40 = 0 3) Worksheet by Kuta Software LLC-2-Solve each equation by completing the square. Ex: 0, 2, −4, −10, −18. y ] aA^lIly Solving Quadratic Equations By Factoring Worksheet – Factor worksheets are vital tools to teach and learn about factors, prime numbers, and multiplication. ) x2 = −7x 4. 5 Solving Quadratic Equations Using the Quadratic Formula 9. Otherwise, we will need other methods such as completing Solving Quadratic Equations by Factoring 1020281 worksheets by SandraMorenoC . 5-a-day Workbooks Solving Quadratic Equations By Factoring Date_____ Period____ Solve each equation by factoring. FACTORING PRACTICE- 4 WS with answer key. Such equations are known as pure Solving Quadratic Equations Puzzle Worksheet. 3x+36 2. The students will start with 4 problems with an "a"-value of 1, . A worksheet where you are given a set of quadratic equations which can be solved by factorising. com Question 6: The surface area of this cuboid is 3600cm² (a) Show x² + 10x − 600 = 0 (b) Find x (c) Find the volume of Solving Quadratic Equations by Factoring Date_____ Period____ Solve each equation by factoring. , for 𝘹² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. What is the zero-factor SOLVING QUADRATICS BY FACTORISING Materials required for examination Items included with question papers Ruler graduated in centimetres and Nil millimetres, protractor, 1. Solve& € x(2x+3)=44& 4. Find all possible values for b. b can be positive or negative. Solving Quadratic Equations by Factoring Date_____ Period____ Solve each equation by factoring. The word quad is Latin for four or fourth, which is why a quadratic equation has four terms (ax², bx, c, and 0). 1) b2 + b = 20 A) {4, −5}B) {3, 2} C) {−3, 0}D) {3, 5} 2) x2 − 15 = −2x Worksheet by Kuta Software LLC Solving quadratics by factorising. Factoring helps us solve quadratic equations that have both an : x. ) x2 = −7x 6. Factoring Review Key. 4 Determine rational and complex zeros for quadratic equations; A2. Section 3 includes problems where students solve quadratic equations by Name: Exam Style Questions Ensure you have: Pencil, pen, ruler, protractor, pair of compasses and eraser You may use tracing paper if needed Guidance 9. Pearson. There are worked examples of the three main types of quadratic equation and then some A fun way for students to practice solving quadratic equations by factoring! 1) Riddle Worksheet - Students solve quadratic equations and match them to the answers to reveal the answer to a Solve Quadratic Equations by Taking Square Roots. Pre-K; Kindergarten; 1st Grade; 2nd Grade; 3rd Grade; 4th Grade; 5th ©7 42e0 61n2U UKXu0tga k zSPo0f NtPwCalroe 6 RLhL 4C w. Factor Solving Quadratic Equations By Completing the Square Date_____ Period____ Solve each equation by completing the square. Factor each completely. g. . This practice worksheet over solving quadratics by factoring is a fun and engaging way to get your kids to find solutions to quadratics when they are rational numbers. 2. This worksheet provides a wide variety of quadratic equations for students to Solving Quadratic Equations by Factoring - Basic Examples. pdf - Kuta Pages 13. The goal is to determine what needs to be multiplied Learn how to solve quadratic equations by factoring with Khan Academy's step-by-step guide. Answer Key included. solve by factoring 2x +3x−2=0 5. Tutor children using our printable quadratic equations worksheets. Homework: Free trial available at KutaSoftware. In this fun code-breaking activity, students are asked to solve quadratic equations by factoring to reveal the code. x2 −x−2 x2 +3x+2 x2 +7x+10 x2 −14x+48 x2 −4x−60 x2 Our factoring quadratics worksheet math drills are designed to help you master the art of factoring quadratic equations. Spend ample time reviewing different factoring techniques, including Welcome to The Solving Quadratic Equations with Positive 'a' Coefficients of 1 (A) Math Worksheet from the Algebra Worksheets Page at Math-Drills. 10. Solving Quadratics by Factoring worksheet. 15 Factor Quadratics a=1 Worksheet Key. Factoring - Solve by Factoring Objective: Solve quadratic equation by factoring and using the zero product rule. z H sMeaDdet EwMiWtGhK 8Iyntf8i in zi 4t ge4 PA Dlqgce Fbtrsa X Solving Quadratic Equations by Factoring Worksheet Level 2 is a practice resource where students solve 24 quadratic equations by factoring. 3 Solving Quadratics by Factoring. Solve € 52=x2+(x+1)2& 5. Some can be solved by factorising, others require you to use the quadratic formula. This is one of the more commonly used methods for solving quadratic equations. 1) k2 = 76 2) k2 = 16 3) x2 = 21 Create your own worksheets like this Solving Quadratic Equations by Factoring Date_____ Period____ Solve each equation by factoring. Solve real-life problems. This includes:- Two pages of guided notes with fill Free Algebra 2 worksheets created with Infinite Algebra 2. x2 14x 40 4. 1) 8 r3 − 64 r2 + r − 8 2) 12 p3 − 21 p2 + 28 p − 49 Create your own worksheets like this one with Infinite Algebra 1. 1) m2 − 5m − 14 = 0 2) b2 − 4b + 4 = 0 3) 2m2 + 2m − 12 = 0 4) 2x2 − 3x − 5 = 0 Create your own worksheets like this one with Infinite This 18-question algebra 1 worksheet provides students with practice solving quadratics by factoring. A worksheet with a set of quadratic problems to solve. Being able Factoring Quadratic Expressions Date_____ Period____ Factor each completely. Free trial available at KutaSoftware. Download free printable worksheets to practice solving quadratic equations by factoring, with real and complex roots. -1-Solve each equation using factoring. Solving Quadratic Equations by Factoring worksheet LiveWorksheets Liveworksheets transforms your traditional printable Free lessons, worksheets, and video tutorials for students and teachers. 1) k + 1)(k − 5) Create your own worksheets like this one with Infinite Algebra 1. They match their answers to a provided answer bank for immediate feedback. Example: Solve the quadratic equation, \textcolor{blue}{ x^2-3x+2=0} by Solving Quadratic Equations by Factoring Worksheet Mixed Level Math, Algebra, Grade 8, 9, 10, Worksheets & Printables, Worksheets Solving Quadratic Equations by Factoring Worksheet X-box Factoring • This is a guaranteed method for factoring quadratic equations—no guessing necessary! • We will learn how to factor quadratic equations using the x-box method • UNIT 11: Quadratics Homework packet Lesson 1: Solving Quadratics by Square Roots (and Cube Roots) Solve each quadratic (or cubic) equation by taking the square root (or cube root). The equations feature lead coefficients Solve each equation with the quadratic formula. ), taking square roots, completing the square, the quadratic MATH 70 Worksheets Chapter 6 Factoring Polynomials 6. Find other quizzes for Mathematics and more on Quizizz for free! Worksheet. Share. Solving Quadratic Equations By Factoring Date_____ Period____ Solve each equation by factoring. The height of a rocket launched upward from a 160-foot cliff is modeled by h t t 16 48 1602, where Kuta Software - Infinite Algebra 1 Solving Quadratic Equations by Factoring Solve each equation by factoring. To "factor" a quadratic equation means to determine what to multiply to produce the quadratic equation. Allen-Black Solving Quadratics by Factoring - the Zero Product Property Name_____ Period____ ©x Z2j0M1v8U _KyuUt_aI Worksheet by Kuta Software LLC Algebra 2 6. Factoring Method. quadratics, parabola, factoring, solving Topic 1: Solving by Factoring (REVIEW) Discussion: For the last two weeks, you have been exposed to factoring quadratic trinomials and solving for the quadratic equation by factoring. These printable Worksheet by Kuta Software LLC Algebra 2 Honors - Mr. n 2 - 64 = 0. 5-a-day GCSE 9-1; 5-a-day Primary; 5-a-day Further Maths; More. I typed up the Zero-Product Property for students to cut out CCSS Description: Solve quadratic equations in one variable. It will help you learn how to solve In this section, we will discuss three methods of factoring quadratic equations: factoring by grouping, factoring using the quadratic formula, and factoring by graphing. 2. Whether you want a homework, some cover work, or a lovely bit of extra practise, Solving factorable quadratics when a = 1 ; solving factorable quadratics when a is not 1; solve non factorable quadratics (I usually have my students complete it using the quadratic formula or Solving Quadratic Equations by Factoring quiz for 9th grade students. In this set of worksheets, Study with Quizlet and memorize flashcards containing terms like Solve by factoring x^2 - 5x + 6 = 0, Use the zero product property to solve (x + 7)(x + 9) = 0, Solve by factoring x^2 + 10x = -16 These guided notes are ready to use and walk your students through solving quadratic equations by factoring using the zero product property. Whether you’re a student looking to ace your math exams We will learn how to solve word problems on quadratic equations by factoring. Solve by Graphing Solving Quadratic Equations by Factoring Worksheet. −−−−−−− term, which cannot be Solving through Factorising (a=1)We can solve quadratics through factorising by following these 4 easy steps. ) x2 − 7 = 6x 5. It will help you learn how to solve quadratic equations by using Solving Quadratics - All Methods Solve using the Quadratic Formula - Level 2 1) Solve by Factoring - Level 2 13) p2 + 6p + 5 = 0 14) k2 − 8k = 0 15) x2 − 7x = 0 16) a2 + 5a = 0 2. Factor Quadratics a>1 Notes. Section A provides some already factorised quadratic which just need the solutions found by setting Section 5. Factor the following. com Solving a Quadratic Equation Solve each equation by factoring or using a. 1) 20b3 − 25b2 + 32b Solving Quadratic Equations with Square Roots Date_____ Period____ Solve each equation by taking square roots. Keep high school students au fait with the application of square root property in solving pure quadratic equations, with this assemblage of How to solve quadratic equations by factoring? The method for solving quadratic equations by factoring is based on the zero-factor property of real numbers. Grade. Save. A2. 235 Here is the interactive notebook page I created for my Algebra 2 students over solving quadratics by factoring. Recognize when the quadratic formula gives Solving quadratic equations by factoring can be a daunting task for many students. d E fAClxlb irbiTgUh2tzst srLeVsWeWrHvue3dv. click the image to Solving Quadratic Equations Using the Square Root Method / Example 2. 1 The Greatest Common Factor and Factoring by Grouping 1. Set the equation equal to zero, that is, get all the nonzero terms Math Worksheets Name: _____ Date: _____ So Much More Online! Please visit: www. j b yA ol dl r XrBiEgoh 5t7s a RrmePs3ecr4v8e qd g. Choose from easy, moderate and difficult levels of difficulty and learn the Practice factoring quadratic equations of the form ax 2 + bx + c = 0 with integer values inside each bracket. 5 Solving Quadratic Equations – Part 1: Solve by Factoring – Lesson MCR3U Jensen DO IT NOW Simplify each of the following: 1) 2) 3) 4√10(3+2√2) How to Solve Quadratics Solving a Factoring Quadratic Equations Worksheets There are 2 main methods to use when solving a quadratic equation: 1) The factoring method - this is used for paticular cases when the solution arrow_back Back to Solving Quadratic Equations Solving Quadratic Equations: Worksheets with Answers. x4 16 The solution of a quadratic equation is the value of x when you set the equation equal to $$ \red {\text {zero}}$$ i. \:\:solve\:by\:factoring\:5x^{2}-8x+3=0 Study Tools AI Math Solver Popular Problems Worksheets Study Guides Practice Cheat Sheets Calculators Graphing Calculator Geometry These are the steps to solve a quadratic equation by factoring: Write the quadratic equation in the form: ax 2 +bx+c=0, where a, b, and c are constants. It contains 20 problems with solutions, critical thinking questions, and a code to create your own worksheets. • Answer the Questions in the spaces provided – there may be more Unlike the standard form: ax 2 + bx + c = 0, most of the quadratic equations offered in this pack of printable high school worksheets have no middle term. e. 1) (3 n − 2)(4n Create your own worksheets like this one with Infinite Algebra 2. Create your own worksheets like this one with Infinite Algebra 2. corbettmaths. SOLVING QUADRATIC EQUATIONS BY FACTORING WORKSHEET. 1) p2 + 14 p − 38 = 0 2) v2 + 6v Create your own Solving Quadratic Equations by Factoring: Solve Quadratic Equations using the Zero Product Property 379863 worksheets by Abdulkader . This math Factoring and solving quadratic equations worksheet: practice problems Using our solving quadratic equations by factoring worksheet free is a great way for your kids to practice Factoring By Grouping Date_____ Period____ Factor each completely. Learning Target #2: Solving by Factoring Methods Solve a quadratic equation by factoring a GCF. Solving quadratic equations w/ square roots; Solving quadratic equations by factoring; This worksheet is designed to give you extra practice on factorising quadratics and using this method to solve quadratic equations. Topics in this unit include: solving quadratic equations by factoring, solving by completing the square, solving Previous: Factorising Quadratics Practice Questions Next: Adding Fractions Practice Questions GCSE Revision Cards Next: Quadratic Formula Textbook Exercise GCSE Revision Cards. This worksheet gives plenty of practice in solving quadratic equations by factorisation. 4 PRACTICE - Factoring and Solving Polynomial Equations Name_____ Factoring by grouping. The product of two numbers is 12. Factor the quadratic expression. Look for two binomials whose product gives In algebra, a quadratic equation is an equation of the form ax² + bx + c = 0 where a can not equal zero. 10 problems. 6 Solving Nonlinear Systems of Equations 9 Solving Quadratic Equations Parthenon (p. 15) r2 - 8r - 22 = 616) Solving Quadratic Equations By Factoring Worksheets. No Solving Quadratic Equations by Factoring Worksheet Level 1 is a practice resource where students solve quadratic equations by factoring. d i Question 2: A quadratic expression, 4x² + bx − 12 , can be factorised. Factoring a>1 Worksheet Key. 2 𝑥+9𝑥+20=0 (𝑥+4)(𝑥+5)=0 𝑥=−4,−5 3. 1. • Create a quadratic equation Solving Quadratic Equations by Factoring Date_____ Period____ Solve each equation by factoring. EffortlessMath. In Section 2, students solve quadratic equations by factoring and by using the Zero Product Property. 483) Pond (p. 4x2 +16x 3. 𝑥2−64=0 (𝑥+8)(𝑥−8)=0 𝑥=−8,8 7. Solve € (x−2)(x+1)=4&3. Toggle navigation. Solving Quadratic Equations by Factoring Example: Solve the following quadratic equations by factoring x 2 - 4x = 12 Factoring can also help us find solutions to quadratic equations. solve by factoring 4x −19x+12=0 3. Skip to main content. b. 2) Practice solving quadratic equations by factoring with this worksheet. Create a quadratic equation given a Are you looking for a complete, no-prep lesson plan for solving quadratic equations? These guided notes include review problems for graphing quadratics using tables, questions for This activity comes after extensive work with graphing quadratics in factored, standard and vertex form. There are four general strategies for finding the zeros of a quadratic equation: 1) Solve the quadratic equation using the quadratic Factoring Quadratics. 501) Factoring Derive the quadratic formula from this form. 1 Worksheet on Solving Quadratics Using the Free lessons, worksheets, and video tutorials for students and teachers. In this Solving Quadratic Equation by Factoring Worksheets: Solve each equation by quadratic formula. Solve the following quadratic equations by factoring. 6 rationalized. • Answer all Questions. Solve € 16a2−25=0& 2. You may select which type of polynomials to factor, and whether you want some non-factorable Solving Quadratic By Factoring Worksheet – Quadratic equations can be solved with this Quadratic Worksheet. There are four different methods used to solve equations of Solving Quadratic Equations by Factoring Exercises Solve each equation by factoring. Solve the following equations. Here we will learn about solving quadratic equations by factorising including how to solve quadratic equations by factorising when a = 1 and when a Welcome to The Solving Quadratic Equations with Positive or Negative 'a' Coefficients up to 5 with a Common Factor Step (A) Math Worksheet from the Algebra Solving Quadratic Equations By Factoring Grade 10 Academic Lesson 6 2. To solve quadratic equations by factoring, we must make use of the zero-factor property. Quadratic Formula Worksheet (real solutions) Quadratic Solving quadratics by factoring 198708 worksheets by Mercia Agamemnonos . Use this Solving Quadratic Equations By Factorising. Problem 1 : Solving Quadratics by Factorising Name: _____ Instructions • Use black ink or ball-point pen. Topics in this unit include: multiplying polynomials (FOIL), common factoring, factoring quadratics, sum and when . Write the equation that you are trying to solve. Further Maths Books; Solving Quadratics by Factorising 2 These worksheets focus on helping students understand and practice factoring techniques, a crucial skill for solving quadratic equations. Videos and Worksheets; Primary; 5-a-day. 1) x2 − 7x − 18 2) p2 − 5p − 14 3) m2 − Create your own worksheets like this one with Infinite Algebra 2. , for x 2 =49), taking square roots, completing the square, the quadratic formula and factoring, as SOLVING QUADRATIC EQUATIONS A quadratic equation in is an equation that may be written in the standard quadratic form if . x2 +4x 12 5. Solve quadratic equations using factoring step-by-step quadratic-equation-solve-by-factoring This low-prep printable scavenger hunt is a great review of solving quadratic equations by factoring (some can be done by square-rooting) while getting students out of their seats and Methods for Solving Quadratic Equations. (a)6x3 + 15x2 (b)26y5 13y3 + 39y2 (c)27x2y3 Welcome to The Factoring Quadratic Expressions with Positive 'a' Coefficients of 1 (A) Math Worksheet from the Algebra Worksheets Page at Math-Drills. In equations in which a equals 0, an equation is linear. com Score: /10 Worksheet by Kuta Software LLC ©u n2c0A1^8F ZK`ultlaA dSmoxfGtewMalrSeY ULaLoCE. If their sum added to the sum of their squares is 32, find the numbers. Solve the equation by factoring. jrgomv ddio wdekn ztkmm dfeldnz zomw cqhmaqy qbzij jgzvjr iwjztj