Factoring Quadratics

Front

What is factoring in algebra?

Back

Factoring is the process of breaking down an expression into simpler components, 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 are the factors of a quadratic expression?

Back

The factors of a quadratic expression are two binomials that multiply to give the original quadratic expression.

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 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 difference of squares?

Back

The difference of squares is a special factoring pattern that states a² - b² = (a - b)(a + b).

Front

How do you factor a quadratic expression of the form ax² + bx + c?

Back

To factor ax² + bx + c, look for two numbers that multiply to ac and add to b, then use these to split the middle term and factor by grouping.

Front

What is the factored form of x² - 16?

Back

The factored form of x² - 16 is (x - 4)(x + 4), using the difference of squares.

Front

What is the factored form of x² + 10x + 21?

Back

The factored form of x² + 10x + 21 is (x + 3)(x + 7).