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 does it mean to factor a quadratic equation?

Back

Factoring a quadratic equation involves rewriting 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 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 ax² + bx + c = 0, factor it into (x - p)(x - q) = 0, and then set each factor equal to zero to find the solutions x = p and x = q.

Front

What are the steps to factor a quadratic expression?

Back

1. Write the expression in standard form (ax² + bx + c). 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

What is the factored form of x² - 9?

Back

The factored form of x² - 9 is (x - 3)(x + 3), which is a difference of squares.

Front

Solve by factoring: z² - 18z + 81 = 0.

Back

z = 9.

Front

Solve: 16a² - 9 = 0.

Back

a = -3/4, 3/4.

Front

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

Back

x = 1.

Front

Convert to factored form and solve: x² - 9x + 20.

Back

Factored form: (x - 4)(x - 5); Solutions: x = 4, 5.