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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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**Remember Lesson 5-3 for Synthetic Division**

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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**Since the remainder is 0, x-3 is a factor of the polynomial.**

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

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

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

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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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Division and Factors When we divide one polynomial by another, we obtain a quotient and a remainder. If the remainder is 0, then the divisor is a factor.

Division and Factors When we divide one polynomial by another, we obtain a quotient and a remainder. If the remainder is 0, then the divisor is a factor.

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