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Remainder and Factor Theorems Section 7.4. The Remainder Theorem If a polynomial f(x) is divided by x-a, the remainder is the constant f(a), and Dividend=quotient.

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Presentation on theme: "Remainder and Factor Theorems Section 7.4. The Remainder Theorem If a polynomial f(x) is divided by x-a, the remainder is the constant f(a), and Dividend=quotient."— Presentation transcript:

1 Remainder and Factor Theorems Section 7.4

2 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)

3 The Remainder Theorem Remember Lesson 5-3 for Synthetic Division

4 The Remainder Theorem Remainder = 1

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

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

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

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

9 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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