The Remainder Theorem and Factor Theorem

# The Remainder Theorem and Factor Theorem - 3.1 The...

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3.1: The Remainder Theorem and Factor Theorem Consider the polynomial function P ( x ) = x 3 - 7 x - 6 . Notice, P (-1) = (-1) 3 - 7(-1) - 6 = -1 + 7 - 6 = 0 So, -1 is called a zero of the function P . We will be interested in finding the zeros of many polynomial functions. L ONG D IVISION OF P OLYNOMIALS Divide. 734 d 3 = 3 734 Check: divisor œ quotient + remainder = dividend Use long division to divide. (4 x + 3 x 2 + x 3 - 5) d ( x - 2) Solution: x - 2 x 2 + 5 x + 14 x 3 + 3 x 2 + 4 x - 5 - x 3 + 2 x 2 5 x 2 + 4 x -5 x 2 + 10 x 14 x - 5 -14 x + 28 23 Answer: x 2 + 5 x + 14 + 23 x - 2

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Use long division to perform the division. (-8 x 2 - 4 x 3 - 5 - 7 x ) d (2 x +1) Check: divisor œ quotient + remainder = dividend
S YNTHETIC D IVISION Synthetic division is a procedure that accomplishes the same result as long division, but without listing the variables that occur in each polynomial. To apply synthetic division, the divisor must be a polynomial of the form x - c , where c is a constant. Use synthetic division to divide.

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The Remainder Theorem and Factor Theorem - 3.1 The...

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