Solving Quadratic Equations by Factoring

Front

What is a quadratic equation?

Back

A quadratic equation is a polynomial equation of the form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

What is the Zero-Product Property?

Back

The Zero-Product Property states that if the product of two factors is zero, then at least one of the factors must be zero.

Front

How do you solve a quadratic equation by factoring?

Back

To solve by factoring, rewrite the equation in the form (x - p)(x - q) = 0, then set each factor equal to zero and solve for x.

Front

What are the steps to factor a quadratic equation?

Back

1. Write the equation in standard form. 2. Find two numbers that multiply to ac and add to b. 3. Rewrite the middle term using these numbers. 4. Factor by grouping.

Front

Solve using Zero-Product Property: (2x - 2)(5x + 5) = 0

Back

x = -1 or x = 1

Front

Solve: x² + 9x + 20 = 0

Back

x = -4, x = -5

Front

Solve using Zero-Product Property: (n + 7)(n + 9) = 0

Back

n = -7; n = -9

Front

What is the first step in solving x² + 6x - 13 = 3?

Back

Make it equal 0 by subtracting 3 on each side.

Front

Solve by factoring: x² + 12x + 35 = 0

Back

x = -5 or x = -7

Front

What does it mean to factor a quadratic equation?

Back

Factoring a quadratic equation means rewriting it as a product of two binomials.