Factoring Linear 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 share. It is used in factoring to simplify expressions.

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 in the expression, divide each term by the GCF, and express the original expression as the product of the GCF and the simplified expression.

Front

What is the factored form of the expression 17xy - x?

Back

x(17y - 1) is the factored form of the expression 17xy - x.

Front

How do you factor the expression -16x - 56?

Back

To factor -16x - 56, first find the GCF, which is -8. Then, factor it out to get -8(2x + 7).

Front

What is the factored form of the expression 8x + 40?

Back

The factored form of the expression 8x + 40 is 8(x + 5).

Front

How do you factor the expression -5b + 25a - 40?

Back

To factor -5b + 25a - 40, find the GCF, which is 5. Factor it out to get 5(-b + 5a - 8).

Front

What is the factored form of the expression -8c - 8?

Back

The factored form of the expression -8c - 8 is -4(2c + 2).

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 the original expression.

Front

What is a linear expression?

Back

A linear expression is an algebraic expression in which the highest power of the variable is one, resulting in a straight line when graphed.