Skill 2 of 12

Solve quadratic equations by factoring

Solve quadratic equations by rewriting in standard form, factoring, and applying the zero-product property.

Common Core standards: A-REI.4bA-SSE.3a
Builds on: Factor quadratic expressions

Common mistakes

What students most often get wrong with this skill:

Applying the zero-product property when the equation is not set equal to zero
Taking the sign of a factor as the root, e.g. $(x+3)=0$ gives $x=3$
Dividing both sides by $x$ and losing the solution $x=0$

A worked example

From the lesson, with every step explained.

Example 1: already set to zero

Problem: Solve $x^2-x-12=0$ .

Plan: The right side is already $0$ , so factor the left side and use the zero-product property.

1) Factor. We need two numbers that multiply to $-12$ and add to $-1$ . Those are $-4$ and $3$ .

(x-4)(x+3)=0

2) Zero-product property: one factor must be $0$ , because the product is $0$ .

x-4=0 \quad\text{or}\quad x+3=0

3) Solve each one.

x=4 \quad\text{or}\quad x=-3

Answer: $x=4$ or $x=-3$ .

Check:

$4^2-4-12=16-4-12=0$ ✓

$(-3)^2-(-3)-12=9+3-12=0$ ✓

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