Factoring Out a GCF

Learn and apply factoring out a gcf using equations, examples, and interpretation.

Lesson 5 of 53 parts Practice Flashcards

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Numerical Common Factor

Objective: Explain and use numerical common factor in an Algebra 1 problem.

The greatest common numerical factor divides every coefficient in the terms; factor it out before looking for further structure. It fully removes the shared numerical part in one step.

Worked examples

Try itExample 1.1: What is the greatest common numerical factor of 10x and 26x²?Show answer

2. Find the greatest integer dividing both coefficients. The answer is 2.

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Numerical Common Factor

Objective: Explain and use numerical common factor in an Algebra 1 problem.

The greatest common numerical factor divides every coefficient in the terms; factor it out before looking for further structure. It fully removes the shared numerical part in one step.

Worked examples

Try itExample 1.1: What is the greatest common numerical factor of 10x and 26x²?Show answer

2. Find the greatest integer dividing both coefficients. The answer is 2.

Variable Common Factor

Objective: Explain and use variable common factor in an Algebra 1 problem.

The shared variable factor uses the smallest exponent appearing in every term, with a zero exponent if a term lacks that variable. No x can be factored from every term.

Worked examples

Try itExample 2.1: What is the greatest common numerical factor of 24x and 69x²?Show answer

3. Find the greatest integer dividing both coefficients. The answer is 3.

Checking by Distribution

Objective: Explain and use checking by distribution in an Algebra 1 problem.

Multiply the proposed GCF back through the remaining expression to verify the original polynomial is recovered. It exposes structure for further solving or simplifying.

Worked examples

Try itExample 3.1: What is the greatest common numerical factor of 44x and 132x²?Show answer

44. Find the greatest integer dividing both coefficients. The answer is 44.

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