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 steps to solve a quadratic equation by factoring?

Back

1. Write the equation in standard form (ax² + bx + c = 0). 2. Factor the quadratic expression. 3. Set each factor equal to zero. 4. Solve for the variable.

Front

Solve by factoring: x² + 3x - 18 = 0

Back

x = 3 and x = -6

Front

Solve by factoring: x² - 9x + 20 = 0

Back

x = 4 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 by factoring: a² + 2a - 24 = 0

Back

a = -6 and a = 4

Front

What is a binomial?

Back

A binomial is a polynomial that contains exactly two terms, such as (x + 3) or (2a - 5).

Front

What is the significance of the coefficients in a quadratic equation?

Back

The coefficients (a, b, c) determine the shape and position of the parabola represented by the quadratic equation.

Front

Solve by factoring: x² - 4 = 0

Back

x = 2 and x = -2