Solving Quadratic Equations by Factoring

Front

What is a quadratic equation?

Back

A quadratic equation is a polynomial equation of degree 2, typically in 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. For example, if (x - 3)(x + 2) = 0, then x - 3 = 0 or x + 2 = 0.

Front

How do you solve a quadratic equation by factoring?

Back

To solve a quadratic equation by factoring, express the equation in the form (x - p)(x - q) = 0, where p and q are the roots. Then set each factor equal to zero and solve for x.

Front

Solve for x: (x + 2)(x - 3) = 0

Back

x = -2 or x = 3.

Front

What are the roots of the equation x² - 5x + 6 = 0?

Back

The roots are x = 2 and x = 3.

Front

Solve for x: x² + 2x - 20 = 0

Back

x = -6 or x = 4.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax² + bx + c = 0.

Front

Solve by factoring: x² - 9x + 20 = 0

Back

x = 4 and x = 5.

Front

What is the first step in solving a quadratic equation by factoring?

Back

The first step is to set the equation equal to zero.

Front

What does it mean to factor a quadratic expression?

Back

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