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 involves rewriting it as a product of two binomials, allowing for easier solutions.

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 factor the equation 6x² - 18x = 0?

Back

Factor out the common term: 6x(x - 3) = 0.

Front

What are the solutions to the equation 6x² - 18x = 0?

Back

The solutions are x = 0 and x = 3.

Front

How do you solve the equation 16x² - 9 = 0 by factoring?

Back

Recognize it as a difference of squares: (4x - 3)(4x + 3) = 0.

Front

What are the solutions to the equation 16x² - 9 = 0?

Back

The solutions are x = -3/4 and x = 3/4.

Front

What is the process to solve x² + 8x - 20 = 0 by factoring?

Back

Factor to (x + 10)(x - 2) = 0.

Front

What are the solutions to the equation x² + 8x - 20 = 0?

Back

The solutions are x = -10 and x = 2.

Front

How do you factor the equation x² - 225 = 0?

Back

Recognize it as a difference of squares: (x - 15)(x + 15) = 0.