Solve by Factoring Worksheet

This solve by factoring worksheet helps students practice factoring quadratic equations and applying the zero product property. The printable set includes 12 randomized questions and an answer key on page 2.

What is Solving by Factoring?

Solving by factoring means rewriting a quadratic equation as a product of two factors equal to zero. Once the equation is factored, you set each factor equal to zero and solve the simpler equations.

How to Solve by Factoring

1. Move all terms to one side so the equation equals zero.
2. Factor the quadratic expression completely.
3. Set each factor equal to zero.
4. Solve each equation to get the roots.

Example

Solve $x^2 + 5x + 6 = 0$

Factor: $(x + 2)(x + 3) = 0$

Set each factor equal to zero:

$x + 2 = 0$ or $x + 3 = 0$

So the solutions are $x = -2$ and $x = -3$.

FAQ

Q: When should I use factoring to solve a quadratic?
A: Factoring works best when the quadratic expression can be broken into integer or simple rational factors.

Q: Why do we set each factor equal to zero?
A: The zero product property says that if two factors multiply to zero, then at least one of the factors must be zero.