Factoring and GCF Flashcard

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 the Greatest Common Factor (GCF)?

Back

The GCF of two or more terms is the largest expression that divides all the terms without leaving a remainder.

Front

How do you factor a quadratic expression of the form x^2 + bx + c?

Back

To factor a quadratic expression of the form x^2 + 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 x^2 - 4?

Back

The factored form of x^2 - 4 is (x - 2)(x + 2), which is a difference of squares.

Front

How do you factor out the GCF from an expression?

Back

To factor out the GCF, identify the largest factor common to all terms, divide each term by the GCF, and express the original expression as the GCF multiplied by the resulting expression.

Front

What is the factored form of 36a^2 + 24a?

Back

The factored form of 36a^2 + 24a is 12a(3a + 2).

Front

What is the first step in factoring a polynomial?

Back

The first step in factoring a polynomial is to look for the GCF of all the terms.

Front

How do you factor the expression 4k^2 + 24k + 36?

Back

First, factor out the GCF, which is 4, to get 4(k^2 + 6k + 9). Then, factor the quadratic to get 4(k + 3)^2.

Front

What is the difference between factoring and expanding an expression?

Back

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

Front

What is a binomial?

Back

A binomial is a polynomial with exactly two terms.