Factoring Quadratics

Front

What is factoring in algebra?

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 does GCF stand for in factoring?

Back

GCF stands for Greatest Common Factor, which is the largest factor that divides two or more numbers or terms.

Front

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

Back

To factor a quadratic expression of the form 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 the two numbers.

Front

What is the factored form of the expression x² - 14x + 24?

Back

The factored form is (x - 12)(x - 2).

Front

What is the factored form of the expression d² - 10d + 25?

Back

The factored form is (d - 5)(d - 5) or (d - 5)².

Front

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

Back

To factor a trinomial of the form ax² + bx + c, look for two numbers that multiply to ac and add to b, then rewrite the middle term and factor by grouping.

Front

What is the factored form of the expression 4x² - 16x - 9?

Back

The factored form is (2x - 9)(2x + 1).

Front

What is the factored form of the expression 5n² - 6n - 27?

Back

The factored form is (5n + 9)(n - 3).

Front

What is the difference between factoring and expanding an expression?

Back

Factoring is breaking down an expression into its factors, while expanding is multiplying out the factors to get back to the original expression.