Factoring Quadratics

Front

What is factoring in mathematics?

Back

Factoring is the process of breaking down an expression into a product of simpler expressions, called factors.

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 are the roots of a quadratic equation?

Back

The roots of a quadratic equation are the values of x that make the equation equal to zero.

Front

What is the standard form of a quadratic equation?

Back

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

Front

How do you solve a quadratic equation by factoring?

Back

To solve by factoring, rewrite the equation in the form (x - p)(x - q) = 0, then set each factor equal to zero and solve for 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

What is the first step in solving x² + 15x + 44 = 0?

Back

Factor the quadratic expression to find the values of x.

Front

How do you factor the expression x² + 15x + 44?

Back

Look for two numbers that multiply to 44 and add to 15; these numbers are 11 and 4.

Front

What are the solutions to the equation (x + 2)(x - 3) = 0?

Back

Set each factor equal to zero: x + 2 = 0 or x - 3 = 0, giving solutions x = -2 and x = 3.

Front

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

Back

Make it equal to zero by subtracting 3 from both sides: x² + 6x - 16 = 0.