FACTOR POLYNOMIALS

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What is the process of factoring by grouping?

Back

Factoring by grouping involves rearranging and grouping terms in a polynomial to factor out common factors from each group, allowing for further simplification.

Front

How do you factor a polynomial of the form ax^2 + bx + c?

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To factor a polynomial of the form ax^2 + bx + c, look for two numbers that multiply to ac and add to b. Rewrite the middle term using these numbers, then factor by grouping.

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

Back

(5n²+3)(n-2)

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What is the factored form of the polynomial x³ - 4x² - 4x + 16?

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(x-4)(x²-4) or (x-4)(x-2)(x+2) after further factoring.

Front

What is the factored form of the polynomial n² + 16n + 63?

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(n+7)(n+9)

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

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(x²-2)(x+7)

Front

What is the factored form of the polynomial 2n² + 13n + 15?

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(2n + 3)(n + 5)

Front

What is the significance of the leading coefficient in polynomial factoring?

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The leading coefficient affects the shape and direction of the polynomial's graph and can influence the factoring process, especially in determining the possible rational roots.

Front

What are the steps to factor a trinomial of the form x² + bx + c?

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1. Identify a, b, and c. 2. Find two numbers that multiply to c and add to b. 3. Rewrite the trinomial as (x + m)(x + n) where m and n are the two numbers.

Front

What is the difference between factoring a polynomial completely and partially?

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Factoring completely means breaking down a polynomial into irreducible factors, while partial factoring may leave some factors in a non-factored form.