Factoring Algebraic Expressions

Front

What is factoring in algebra?

Back

Factoring in algebra 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 greatest common factor (GCF) is the largest factor that two or more numbers or expressions share. It is used to simplify expressions by factoring out the GCF.

Front

How do you factor the expression 24g - 12h + 36?

Back

To factor the expression 24g - 12h + 36, first find the GCF, which is 12. Then, factor it out: 12(2g - h + 3).

Front

What is the factored form of 10x + 2xy?

Back

The factored form of 10x + 2xy is 2x(5 + y).

Front

How do you factor out a negative term from an expression?

Back

To factor out a negative term, you take the negative sign out of the expression and adjust the remaining terms accordingly. For example, from -2d - 7, you can factor out -1 to get -1(2d + 7).

Front

What is the factored form of -4x - 20?

Back

The factored form of -4x - 20 is -4(x + 5).

Front

How do you factor the expression 8t - 32u?

Back

To factor the expression 8t - 32u, find the GCF, which is 8, and factor it out: 8(t - 4u).

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.

Front

What is a polynomial?

Back

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

Front

What does it mean to simplify an expression?

Back

Simplifying an expression means to reduce it to its simplest form, which often involves combining like terms and factoring.