7.2.4 Flashcard Review: Factoring Algebraic Expressions

Front

What is the Greatest Common Factor (GCF)?

Back

The GCF is the largest number that divides two or more numbers without leaving a remainder.

Front

How do you factor the expression 8xy + 16y using the GCF?

Back

The GCF of 8xy and 16y is 8y. Factoring gives: 8y(x + 2).

Front

What is the area of a rectangle?

Back

The area of a rectangle is calculated by multiplying its length by its width.

Front

If a rectangle has an area of (12m - 30n) and a width of 6, how do you find the length?

Back

Factor the area expression: (12m - 30n) = 6(2m - 5n). The length is (2m - 5n).

Front

What does it mean to factor an expression completely?

Back

Factoring completely means breaking down an expression into its simplest form, where no further factoring is possible.

Front

Factor the expression 24g - 12h + 36.

Back

The expression can be factored as 12(2g - h + 3).

Front

What is the first step in factoring the expression 18k + 42?

Back

Identify the GCF, which is 6, and factor it out: 6(3k + 7).

Front

How do you factor the expression 10x + 2xy?

Back

The GCF is 2x. Factoring gives: 2x(5 + y).

Front

What is a polynomial?

Back

A polynomial is a mathematical expression that consists of variables, coefficients, and exponents, combined using addition, subtraction, and multiplication.

Front

What is the difference between factoring and expanding an expression?

Back

Factoring breaks an expression into simpler components, while expanding multiplies out the components to form a single expression.