Factoring by Greatest Common Factor (GCF)

Front

What is the Greatest Common Factor (GCF)?

Back

The GCF is the largest positive integer that divides all the given numbers without leaving a remainder.

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How do you find the GCF of two numbers?

Back

To find the GCF, list the factors of each number and identify the largest factor that appears in both lists.

Front

Factor the expression using GCF: 8n^3 + 2n^2

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2n^2(4n + 1)

Front

Factor the expression: 6x^2y - 18xy^2

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6xy(x - 3y)

Front

Factor the expression: -9x + 33

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3(-3x + 11)

Front

Factor completely: 5x^2 + 20

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5(x^2 + 4)

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Factor the expression: 4b^5 + 4b^3 + 16b^2

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4b^2(b^3 + b + 4)

Front

What is the first step in factoring by GCF?

Back

Identify the GCF of all the terms in the expression.

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Why is factoring by GCF important?

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It simplifies expressions and makes it easier to solve equations or further factor the expression.

Front

What does it mean to factor an expression completely?

Back

To factor an expression completely means to break it down into its simplest factors, where no further factoring is possible.