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 expression?

Back

A quadratic expression is a polynomial of degree 2, typically in the form ax² + bx + c, where a, b, and c are constants.

Front

What are the factors of x² - 81?

Back

(x - 9)(x + 9) - This is a difference of squares.

Front

How do you factor a quadratic expression in the form x² + bx + c?

Back

Look for two numbers that multiply to c and add to b, then express the quadratic as (x + m)(x + n) where m and n are those numbers.

Front

What is the zero-product property?

Back

If the product of two factors is zero, then at least one of the factors must be zero.

Front

How do you solve a quadratic equation by factoring?

Back

1. Factor the quadratic expression. 2. Set each factor equal to zero. 3. Solve for the variable.

Front

What are the roots of a quadratic equation?

Back

The roots are the values of x that make the equation equal to zero, found by solving the equation.

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the roots of a quadratic equation.

Front

What does it mean for a quadratic to be factorable?

Back

A quadratic is factorable if it can be expressed as a product of two binomials with rational coefficients.

Front

What are the factors of 3x² - 17x + 10?

Back

(x - 5)(3x - 2) - Found by identifying two numbers that multiply to 30 and add to -17.