Factoring Common Binomial Factors in Algebra

This tutorial covers factoring out a common binomial factor, similar to factoring a monomial. It includes examples demonstrating how to identify and factor out common binomial terms, such as x - 3, t^2 + 4, and x + 4. The tutorial also addresses cases where no common factor exists and provides mixed review examples for practice.

What is the common binomial factor in the expression 7(x - 3) - 2x(x - 3)?

• 7 - 2x

• x + 3

• 3x - 7

• x - 3

After factoring out the common binomial from the expression in Example A, what remains inside the new parentheses?

• 7x + 2

• 7 + 2x

• 7x - 2

• 7 - 2x

In Example B, what is factored out from the expression -t(t^2 + 4) + (t^2 + 4)?

• -t + 1

• t(t^2 + 4)

• t^2 - 4

• t^2 + 4

What expression is left after factoring out from the problem in Example B?

• t + 1

• -t - 1

• -t + 1

• t - 1

In Example C, which expressions are shown to be equivalent?

• x - 4 and 4 - x

• x + 4 and 4 + x

• 9x and -5

• x^2 and 4x

What is the result after factoring out the common expression in Example C?

• 9x - 5

• 9x + 5

• 5 - 9x

• 5 + 9x

Why can't the expression in Example D be factored?

• All terms are unique

• Only variable factors

• Only numerical factors

• No common factors

What is the common factor in Example E?

• 4s - 5

• s - 6

• 5s + 6

• s + 6

What remains after factoring out the common factor in Example E?

• 4s - 5

• 5s + 4

• 5s - 4

• 4s + 5

Identify the common factor in Example F.

• 7x + 2

• 2x + 3

• 7x - 2

• 2x - 3