Factoring Algebraic Expressions

Front

What is factoring in algebra?

Back

Factoring is the process of breaking down an expression into a product of simpler expressions, called factors.

Front

What is a common factor?

Back

A common factor is a number or expression that divides two or more numbers or expressions evenly.

Front

Factor the expression: 12a^3b^3 + 6a^2b^3 + 9a^3b^2

Back

3a^2b^2(4ab + 2b + 3a)

Front

What is the greatest common factor (GCF)?

Back

The GCF is the largest factor that two or more numbers or expressions share.

Front

Factor the expression: 6a^2b + 4ab^2 + 2ab

Back

2ab(3a + 2b + 1)

Front

What does it mean to factor an expression completely?

Back

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

Front

Factor the expression: 7x^3 + 4x^5

Back

x^3(7 + 4x^2)

Front

What is a polynomial?

Back

A polynomial is an algebraic expression that consists of variables, coefficients, and non-negative integer exponents.

Front

Factor the expression: 14a^3b^4 + 6a^3b^2 + 8a^3b^3

Back

2a^3b^2(7b^2 + 3 + 4b)

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 form a sum.