Factoring by Grouping

Front

What is factoring by grouping?

Back

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

Front

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 the expression: 4p³ + 8p² + 3p + 6

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(4p² + 3)(p + 2)

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Factor the expression: 3x³ - x² + 6x - 2

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(x² + 2)(3x - 1)

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Factor the expression: 5n³ - 10n² + 3n - 6

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(5n² + 3)(n - 2)

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Factor the expression: x³ + 7x² - 2x - 14

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(x² - 2)(x + 7)

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Factor the expression: 28x² + 63x + 12x + 27

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(7x + 3)(4x + 9)

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What is a common factor?

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A common factor is a number or expression that divides two or more numbers or expressions evenly.

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 the terms.

Front

What is the purpose of factoring a polynomial?

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Factoring a polynomial simplifies it and can help in solving equations or finding roots.