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 for x by factoring: x² - 5x + 6 = 0

Back

x = 2 and x = 3

Front

Solve for x by factoring: x² + 7x + 10 = 0

Back

x = -2 and x = -5

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

Solve for a by factoring: a² + 2a - 24 = 0

Back

a = -6 and a = 4

Front

Solve for x by factoring: x² + 3x - 18 = 0

Back

x = 3 and x = -6

Front

Solve for x by factoring: x² - 9x + 20 = 0

Back

x = 4 and x = 5