Factoring by Grouping

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What is factoring by grouping?

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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?

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The first step is to group the terms of the polynomial into pairs or sets that have common factors.

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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: 7r³ - 8r² + 42r - 48

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(r² + 6)(7r - 8)

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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: x³ - 4x² - 4x + 16

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(x - 4)(x² - 4)

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Factor the expression: 20x³ - 25x² + 4x - 5

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(5x² + 1)(4x - 5)

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What is a common factor?

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A common factor is a number or variable that divides two or more terms without leaving a remainder.

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What does it mean to factor a polynomial?

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Factoring a polynomial means to express it as a product of its factors.

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What is the significance of the distributive property in factoring?

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The distributive property allows us to factor out common terms from grouped expressions.