Factoring Expressions

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 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 12x + 8y - 4z?

Back

4(3x + 2y - z) is the factored form of the expression.

Front

How do you factor the expression 9x - 81?

Back

Factor out the GCF, which is 9, to get 9(x - 9).

Front

What is the factored form of the expression 4x + 30?

Back

2(2x + 15) is the factored form of the expression.

Front

How do you factor the expression 2y + 2?

Back

Factor out the GCF, which is 2, to get 2(y + 1).

Front

What is the factored form of the expression 21x - 36?

Back

3(7x - 12) is the factored form of the expression.

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 are the steps to factor a polynomial expression?

Back

1. Identify the GCF. 2. Factor out the GCF. 3. Look for patterns (like difference of squares, trinomials, etc.). 4. Continue factoring until no further factoring is possible.