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 us to find its roots or solutions.

Front

What is the standard form of a quadratic equation?

Back

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

Front

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

Back

The first step is to set the equation to zero and, if possible, factor out the greatest common factor (GCF).

Front

How do you find the roots of a factored quadratic equation?

Back

Set each factor equal to zero and solve for the variable.

Front

What is the relationship between the coefficients and the roots of a quadratic equation?

Back

For a quadratic equation ax² + bx + c = 0, the sum of the roots is -b/a and the product of the roots is c/a.

Front

Solve by factoring: x² + 4x - 32 = 0

Back

x = -8, 4

Front

Solve by factoring: 3x² + 18x + 15 = 0

Back

x = -5, -1

Front

Solve by factoring: x² = 9x - 20

Back

x = 4, 5

Front

Solve by factoring: 5x² + 13x + 6 = 0

Back

x = -2, -3/5