FACTOR POLYNOMIALS

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What is the process of factoring by grouping?

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Factoring by grouping involves rearranging and grouping terms in a polynomial to factor out common factors from each group, ultimately simplifying the expression.

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How do you factor a quadratic expression of the form ax² + bx + c?

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To factor a quadratic expression of the form ax² + bx + c, look for two numbers that multiply to ac (the product of a and c) and add to b. Rewrite the middle term using these numbers and factor by grouping.

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What are the steps to factor a polynomial completely?

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1. Look for a common factor in all terms. 2. If it's a quadratic, use the quadratic formula or factoring methods. 3. For higher degree polynomials, use synthetic division or polynomial long division if necessary.

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What is the factored form of x² - 10x + 9?

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(x - 9)(x - 1) is the factored form of x² - 10x + 9.

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What is the factored form of 5n³ - 10n² + 3n - 6?

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(5n² + 3)(n - 2) is the factored form of 5n³ - 10n² + 3n - 6.

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What is the significance of the zero product property in factoring?

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The zero product property states that if the product of two factors is zero, at least one of the factors must be zero. This is used to find the roots of polynomial equations after factoring.

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How do you factor the expression x³ - 4x² - 4x + 16?

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First, group the terms: (x³ - 4x²) + (-4x + 16). Factor out common factors from each group to get (x - 4)(x² - 4). Further factor x² - 4 as (x - 2)(x + 2), leading to the complete factorization (x - 4)(x - 2)(x + 2).

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What is the factored form of 2m² + 3m - 9?

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(m + 3)(2m - 3) is the factored form of 2m² + 3m - 9.

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What is a common factor in polynomial expressions?

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A common factor is a number or variable that divides all terms of a polynomial without leaving a remainder. It can be factored out to simplify the expression.

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What is the difference between factoring and expanding polynomials?

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Factoring is the process of breaking down a polynomial into simpler components (factors) that multiply to give the original polynomial, while expanding is the process of multiplying out the factors to obtain the polynomial.