Question

For the given polynomial P(x) and the given c, use the remainder theorem to find P(c).

P(x) = 5x³-4x² -5x+7; -2
P(c) =
(Simplify your answer.)
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Answer 1

To find P(c) for P(x) = 5x³ - 4x² - 5x + 7 when c = -2, substitute -2 into the polynomial according to the Remainder Theorem, yielding P(-2) = -39.

To find P(c) for the given polynomial P(x) = 5x³ - 4x² - 5x + 7 at the given value c = -2, we use the Remainder Theorem. This theorem states that the remainder of the division of a polynomial by a linear divisor x - c is the value of the polynomial at c, P(c). In this case, we simply substitute -2 into the polynomial:

P(-2) = 5(-2)³ - 4(-2)² - 5(-2) + 7

P(-2) = 5(-8) - 4(4) + 10 + 7

P(-2) = -40 - 16 + 10 + 7

P(-2) = -39

Therefore, P(-2) is -39.