﻿ How to Solve Quadratic Equation by factoring. Video Tutorial, practice problems plus worksheet with answer key

# Solve a quadratic equation by factoring

Step by Step Examples

A quadratic equation is an equation that can be written as:

ax ² + bx + c where a ≠ 0

A quadratic equation must have a squared term as its highest power

1. y = 2x² + 3x + 7
2. y = 13x² + 2
3. y = x² − 4x + 15
4. y = −x² + 5

### Examples of Equations that are NOT Quadratic

1. y = 11x + 223
2. y = x3 − 4x² +5x +6
3. y = 2x3 − 7x²
4. y = −x4 + 5

The solution of a quadratic equation is the value of x when you set the equation equal to zero
i.e. When you solve the following general equation:0 = ax² + bx + c

Given a quadratic equation:ax ² + bx + c

One method to solve the equation for zero is to factor the equations.

### General Steps to solve by factoring

Create a factor chart for all factor pairs of c

A factor pair is just two numbers that multiply and give you c

1. Out of all of the factor pairs from step 1, look for the pair (if it exists) that add up to b

Note: if the pair does not exist, you must either complete the square or use the quadratic formula.

2. Insert the pair you found in step 2 into two binomals

Solve each binomial for zero to get the solutions of the quadratic equation.

### Example of how to solve a quadratic equation by factoring

Quadratic Equation: y = x² + 2x + 1

Below is a picture representing the graph of y = x² + 2x + 1

as well as the solution we found by factoring

Below is a picture of the graph of the quadrtaic y = x² − 2x + 1

as well as the solutions

Below is a picture of the graph of the quadrtaic y = x² − 2x + 1 as well as the solutions

y = x² − 4x − 4

is graphed below as well as its solution (2,0)

xy = x² + 6x + 9

is graphed below as well as its solution (2,0)

y = x² − 6x + 9

• c = 9
• b = 6
• The only factors of c whose sum is b are -3 • -3
• y = (x − 3)(x − 3)
• 0 =(x − 3)
• The solution is at x = 3

y = x² + 2x − 3

is graphed below as well as both the solutions

y = x² − 2x − 3

is graphed below as well as both the solutions

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