Solving Quadratic Equations Using Factoring - Varsity Tutors

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Solving Quadratic Equations using Factoring

Study Guide

Key Definition

To solve a quadratic equation using factoring, transform it into standard form $ax^2 + bx + c = 0$.

Important Notes

  • Ensure the equation is in the format $ax^2 + bx + c = 0$
  • Factoring involves finding two binomials that multiply to give the quadratic expression.
  • Set each factor equal to zero to solve for $x$.
  • $(x - r)(x - s) = 0$ implies $x = r$ or $x = s$
  • Check solutions by substituting back into the original equation.

Mathematical Notation

$+$ represents addition$-$ represents subtraction$\times$ or $*$ represents multiplication$\div$ or $/$ represents divisionRemember to use proper notation when solving problems

Why It Works

Factoring exploits the zero product property: if $ab = 0$, then $a = 0$ or $b = 0$.

Remember

Always check your solutions by plugging them back into the original equation.

Quick Reference

Zero Product Property:$ab = 0 \Rightarrow a = 0 \text{ or } b = 0$

Understanding Solving Quadratic Equations using Factoring

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Video explanation of this concept

concept. Use space or enter to play video.concept thumbnailBeginner

Start here! Easy to understand

BeginnerIntermediateAdvanced

Beginner Explanation

Begin by looking at simple quadratics of the form $x^2 + bx + c = 0$. Your goal is to find two numbers that multiply to $c$ and add to $b$. Then write the expression as $(x + m)(x + n)$, set each factor equal to zero, and solve for $x$.Now showing Beginner level explanation.

Practice Problems

Test your understanding with practice problems

1

Quick Quiz

Single Choice QuizBeginner

What is the solution to $(x - 5)(x + 2) = 0$?

A$x = 5 \text{ or } x = -2$B$x = 5 \text{ or } x = 2$C$x = -5 \text{ or } x = 2$D$x = -5 \text{ or } x = -2$Check AnswerPlease select an answer for all 1 questions before checking your answers. 1 question remaining.2

Real-World Problem

Question ExerciseIntermediate

Teenager Scenario

Suppose you are designing a rectangular garden, and the area is given by $2x^2 + 5x = 12$. What are the possible values for $x$?Show AnswerClick to reveal the detailed solution for this question exercise.3

Thinking Challenge

Thinking ExerciseIntermediate

Think About This

Factor the quadratic equation $x^2 - 6x + 9 = 0$ and find the value of $x$.

Show AnswerClick to reveal the detailed explanation for this thinking exercise.4

Challenge Quiz

Single Choice QuizAdvanced

Solve the equation $3x^2 - 12x - 15 = 0$ by factoring.

A$x = 5 \text{ or } x = -1$B$x = 5 \text{ or } x = 1$C$x = -5 \text{ or } x = 1$D$x = -5 \text{ or } x = -1$Check AnswerPlease select an answer for all 1 questions before checking your answers. 1 question remaining.

Recap

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