Factoring by Grouping

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What is factoring by grouping?

Back

Factoring by grouping is a method used to factor polynomials by grouping terms with common factors together.

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What is the first step in factoring by grouping?

Back

The first step is to rearrange the polynomial into two groups that can be factored separately.

Front

Factor by grouping: x³ - 5x² + 5x - 25

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(x² + 5)(x - 5)

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Factor by grouping: 5n³ - 10n² + 3n - 6

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(5n² + 3)(n - 2)

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Factor by grouping: 3x³ - x² + 6x - 2

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(x² + 2)(3x - 1)

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Factor by grouping: 7r³ - 8r² + 42r - 48

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(r² + 6)(7r - 8)

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What is a common factor?

Back

A common factor is a number or expression that divides two or more numbers or expressions without leaving a remainder.

Front

How do you identify common factors in a polynomial?

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Look for the greatest common factor (GCF) among the coefficients and the variables in each term.

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What is the purpose of factoring a polynomial?

Back

Factoring a polynomial simplifies expressions and helps solve equations more easily.

Front

What does it mean to rearrange terms in a polynomial?

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Rearranging terms means changing the order of the terms to group them in a way that makes factoring easier.