Question

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

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

After simplifying the given polynomial to P(x) = x² - 5x + 7, the Remainder Theorem is used to substitute -2 for x, resulting in P(-2) = 21.

Step-by-step explanation:

The question involves using the Remainder Theorem to find the value of a polynomial at a given point. First, let's correct the polynomial. The question shows the polynomial as P(x) = 5x² - 4x² - 5x + 7, which simplifies to P(x) = x² - 5x + 7. According to the Remainder Theorem, in order to find P(c), we simply substitute the given value of c into the polynomial P(x).

In this case, the given value for c is -2. Substitution yields:

P(-2) = (-2)² - 5(-2) + 7 = 4 + 10 + 7 = 21.

Therefore, P(-2) = 21.