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Solving Quadratic Equations using Factoring

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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 division

Remember 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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Watch & Learn

Video explanation of this concept

Beginner

Start here! Easy to understand

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 $x$.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

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

Real-World Problem

Question Exercise

Intermediate

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 $x$?

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

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

Challenge Quiz

Single Choice Quiz

Advanced

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

Recap

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Review key concepts and takeaways