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Use synthetic division and the Remainder Theorem to evaluate P(c)

Use synthetic division and the Remainder Theorem to evaluate P(c), where 

P(x)=x^4 + 7 x^3 + 3 x^2 + 27 x + 48 ,  cC7

quotient =?

remainder=?

p(c)= ?

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1 Answer

You want P(7), so divide P(x) by x - 7.

                   1   14   101    734

1   -7  |  1    7     3      27      48

             1   -7

                  14    3

                  14  -98

                        101    27

                        101  -707

                                 734     48

                                 734  -5138

                                          5186

Thus you get a quotient of x3 + 14x2 + 101x + 734, and a remainder of P(7) = 5186.