How to Factor Quadratics

Factoring turns a quadratic expression into multiplied pieces. It is useful for solving equations, graphing parabolas, and simplifying algebra.

Quick idea

For simple quadratics, find two numbers that multiply to the constant term and add to the middle coefficient.

Steps

1. Check whether there is a greatest common factor.
2. For x squared plus bx plus c, find two numbers that multiply to c and add to b.
3. Write the factors as two binomials.
4. Multiply back to check.

Worked example

Factor x squared plus 5x plus 6.

Full solution

Step-by-step walkthrough

Step 1

Look for two numbers that multiply to 6 and add to 5.

Step 2

The numbers are 2 and 3.

Step 3

So the factors are x plus 2 and x plus 3.

Common mistake

Always check by multiplying the binomials back together. This catches sign mistakes quickly.

Practice problems

1. Factor x^2 + 7x + 12.
2. Factor x^2 - 5x + 6.
3. Factor x^2 + 2x - 8.

Answers

1. (x + 3)(x + 4)
2. (x - 2)(x - 3)
3. (x + 4)(x - 2)

Ask Pennpaper to explain it live

If the steps make sense but you still feel stuck, start a Pennpaper lesson and ask the tutor to draw the problem on the whiteboard. Seeing the symbols move step by step is often what makes the concept click.

Related guides

• The Quadratic Formula Explained
• How to Simplify Exponents
• How to Solve Equations With Variables on Both Sides