Factoring Polynomials

Front

What is factoring in the context of polynomials?

Back

Factoring is the process of breaking down a polynomial into simpler components (factors) that, when multiplied together, give the original polynomial.

Front

What is the factored form of a polynomial?

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The factored form of a polynomial expresses it as a product of its factors, which can be linear or quadratic expressions.

Front

How do you factor out the greatest common factor (GCF) from a polynomial?

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To factor out the GCF, identify the largest factor common to all terms in the polynomial and divide each term by this factor, then express the polynomial as the product of the GCF and the remaining polynomial.

Front

What is the difference of squares, and how is it factored?

Back

The difference of squares is a special case of factoring where a polynomial is in the form a^2 - b^2, which can be factored as (a + b)(a - b).

Front

What is the quadratic formula, and how is it related to factoring?

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The quadratic formula, x = (-b ± √(b² - 4ac)) / (2a), provides the roots of a quadratic equation ax² + bx + c = 0, which can help in factoring the polynomial if the roots are rational.

Front

What is synthetic division, and when is it used in factoring?

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Synthetic division is a simplified method of dividing a polynomial by a linear factor (x - c) and is used to find the quotient and remainder, aiding in the factoring process.

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

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

Front

How do you factor a polynomial by grouping?

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To factor by grouping, divide the polynomial into groups, factor out the GCF from each group, and then factor out the common binomial factor.

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What is the role of the leading coefficient in factoring polynomials?

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The leading coefficient affects the methods used for factoring, especially in trinomials, where it may require techniques like trial and error or the use of the AC method.

Front

What is the AC method in factoring trinomials?

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The AC method involves multiplying the leading coefficient (a) by the constant term (c) and finding two numbers that multiply to this product and add to the middle coefficient (b), then rewriting the trinomial.