Solve Quadratics by Factoring When a=1

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 solve a quadratic equation by factoring?

Back

To solve a quadratic equation by factoring means to express the equation in the form (px + q)(rx + s) = 0 and then use the Zero-Product Property to find the values of x.

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 quadratic x² + 3x - 18?

Back

To factor x² + 3x - 18, find two numbers that multiply to -18 and add to 3. The factors are (x + 6)(x - 3).

Front

What are the solutions to the equation x² + 3x - 18 = 0?

Back

The solutions are x = 3 and x = -6.

Front

What is the first step in solving x² + 6x - 13 = 3?

Back

The first step is to make it equal to 0 by subtracting 3 from both sides, resulting in x² + 6x - 16 = 0.

Front

How do you solve (2x - 2)(5x + 5) = 0 using the Zero-Product Property?

Back

Set each factor to zero: 2x - 2 = 0 gives x = 1, and 5x + 5 = 0 gives x = -1.

Front

What are the solutions to the equation (2x - 2)(5x + 5) = 0?

Back

The solutions are x = 1 and x = -1.

Front

How do you factor the quadratic x² + 2x - 20?

Back

To factor x² + 2x - 20, find two numbers that multiply to -20 and add to 2. The factors are (x + 6)(x - 4).

Front

What are the solutions to the equation x² + 2x - 20 = 4?

Back

The solutions are x = 4 and x = -6.