Factoring Quadratics

Front

What is factoring in mathematics?

Back

Factoring is the process of breaking down an expression into a product of simpler expressions, or factors, that when multiplied together give the original expression.

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 is the standard form of a quadratic equation?

Back

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

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.

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 a quadratic expression of the form x² + bx + c?

Back

To factor x² + bx + c, find 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 two numbers.

Front

What is the factored form of 5x² - 28x + 32?

Back

(5x - 8)(x - 4)

Front

How do you factor a polynomial with a common factor?

Back

To factor a polynomial with a common factor, identify the greatest common factor (GCF) and factor it out from each term.

Front

What is the factored form of 5x³ - 7x²?

Back

x²(5x - 7)

Front

What is the factored form of 17xy - x?

Back

x(17y - 1)