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, allowing for easier factorization.

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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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How do you factor the expression 3x^2 + 15x + xy + 5y?

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You can factor it by grouping as (x + 5)(3x + y) or (3x + y)(x + 5).

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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 x³ + 7x² - 2x - 14?

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The factored form is (x² - 2)(x + 7).

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How do you factor the expression 5n^3 - 10n^2 + 3n - 6?

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You can factor it as (5n^2 + 3)(n - 2).

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What is the factored form of x^3 - 4x^2 - 4x + 16?

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

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What is a common factor in the context of factoring polynomials?

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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 is the significance of the distributive property in factoring?

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The distributive property allows us to factor out common terms from a polynomial, making it easier to simplify and solve.

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What does it mean to factor a polynomial completely?

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Factoring a polynomial completely means breaking it down into irreducible factors, which cannot be factored further.