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Remainder and Factor Theorems Section 7.4

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The Remainder Theorem If a polynomial f(x) is divided by x-a, the remainder is the constant f(a), and Dividend=quotient *divisor +remainder Where is a polynomial with degree one less than the degree of f(x)

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The Remainder Theorem Remember Lesson 5-3 for Synthetic Division

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The Remainder Theorem Remainder = 1

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Your Turn: Use synthetic substitution to find g(3) for the function:

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The Factor Theorem Since the remainder is 0, x-3 is a factor of the polynomial.

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When you divide the polynomial by one of the binomial factors, the quotient is called a depressed equation. The Factor Theorem

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(x-2) Is NOT a factor Remainder = 6, therefore

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The Factor Theorem Given a polynomial and one of its factors, find the remaining factors of the polynomial. Some factors may not be binomials.

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