Factoring by grouping

Front

What is factoring by grouping?

Back

Factoring by grouping is a method used to factor polynomials by grouping terms in pairs and factoring out the common factors from each pair.

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How do you factor the expression x^3 + 7x^2 - 2x - 14 by grouping?

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Group the terms: (x^3 + 7x^2) + (-2x - 14). Factor out common factors: x^2(x + 7) - 2(x + 7). The factored form is (x^2 - 2)(x + 7).

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What is the first step in factoring by grouping?

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

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When factoring the polynomial 6n^3 + 3n^2 + 8n + 4, what common factor can be factored out from the first two terms?

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The common factor from the first two terms (6n^3 + 3n^2) is 3n^2.

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What is the result of factoring the polynomial 3x^3 - 4x^2 + 9x - 12?

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The result is (x^2 + 3)(3x - 4).

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How can you verify if (5x - 4) is a factor of the polynomial 5x^3 - 4x^2 - 25x + 20?

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You can use polynomial long division or synthetic division to divide the polynomial by (5x - 4). If the remainder is 0, then it is a factor.

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What is a binomial?

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A binomial is a polynomial that contains exactly two terms.

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What is the significance of finding common factors in factoring by grouping?

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Finding common factors allows you to simplify the polynomial and make it easier to factor completely.

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What is the factored form of the polynomial 12x^3 + 2x^2 - 30x - 5?

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The factored form is (2x^2 - 5)(6x + 1).

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What does it mean if a polynomial is factorable?

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A polynomial is factorable if it can be expressed as a product of two or more polynomials of lower degree.