Solving Quadratics 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 does it mean to factor a quadratic equation?

Back

Factoring a quadratic equation means expressing it as a product of two binomials, such as (x - p)(x - q) = 0, where p and q are the roots of the equation.

Front

What are the roots of a quadratic equation?

Back

The roots of a quadratic equation are the values of x that make the equation equal to zero.

Front

How do you find the roots of a quadratic equation by factoring?

Back

To find the roots 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

Solve by factoring: x² + 7x + 12 = 0

Back

x = -3, x = -4

Front

Solve by factoring: x² + 3x - 18 = 0

Back

x = 3, x = -6

Front

Solve by factoring: x² - 6x + 5 = 0

Back

x = 5, x = 1

Front

Solve by factoring: z² - 18z + 81 = 0

Back

z = 9

Front

Solve by factoring: k² - 2k - 24 = 0

Back

k = -4, k = 6

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.