4.4 Factoring Higher Degree Polynomials

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What is the definition of factoring in mathematics?

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Factoring is the process of breaking down an expression into a product of simpler expressions, or factors, that when multiplied together give the original expression.

Front

What is a polynomial?

Back

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

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What does it mean to factor a polynomial completely?

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To factor a polynomial completely means to express it as a product of irreducible polynomials, meaning it cannot be factored further over the given number system.

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What is the difference between a monomial and a polynomial?

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A monomial is a polynomial with only one term, while a polynomial can have multiple terms.

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What is the Factor Theorem?

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The Factor Theorem states that if a polynomial f(x) has a factor (x - c), then f(c) = 0.

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What is the Remainder Theorem?

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The Remainder Theorem states that when a polynomial f(x) is divided by (x - c), the remainder is f(c).

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How do you factor a sum of cubes?

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A sum of cubes can be factored using the formula: a^3 + b^3 = (a + b)(a^2 - ab + b^2).

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How do you factor a difference of cubes?

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A difference of cubes can be factored using the formula: a^3 - b^3 = (a - b)(a^2 + ab + b^2).

Front

What is the first step in factoring a polynomial?

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The first step in factoring a polynomial is to look for a greatest common factor (GCF) among the terms.

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What is synthetic division?

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Synthetic division is a simplified form of polynomial long division that is used when dividing by a linear factor.