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 and then factoring out the common binomial.

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How do you determine if a binomial is a factor of a polynomial?

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To determine if a binomial is a factor of a polynomial, you can use polynomial long division or synthetic division. If the remainder is zero, then the binomial is a factor.

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What is the first step in factoring by grouping?

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

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What is the factored form of the polynomial 4p^3 + 8p^2 + 3p + 6?

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The factored form is (4p^2 + 3)(p + 2).

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What is the factored form of the polynomial x³ + 7x² - 2x - 14?

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The factored form is (x² - 2)(x + 7).

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What is the significance of the common factor in factoring by grouping?

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The common factor allows you to simplify the polynomial into a product of simpler polynomials, making it easier to solve or analyze.

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How do you factor the polynomial 6n^3 + 3n^2 + 8n + 4 by grouping?

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Group the terms: (6n^3 + 3n^2) + (8n + 4), factor out common factors from each group, resulting in (3n^2 + 4)(2n + 1).

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What is the factored form of the polynomial 3x^3 - 4x^2 + 9x - 12?

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

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What is a polynomial?

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A polynomial is a mathematical expression consisting of variables, coefficients, and non-negative integer exponents, combined using addition, subtraction, and multiplication.

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What is a binomial?

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A binomial is a polynomial with exactly two terms, such as (a + b) or (x - 3).