Remainder and Factor Theorems

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Remainder and Factor Theorems

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Remainder and Factor Theorems

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)

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

The Remainder Theorem Remainder = 1

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.

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

The Factor Theorem Remainder = 10, therefore (x-2) Is NOT a factor

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