Question

Dividing the polynomial P(x) by x+5 yields a quotient Q(x) and a remainder 6 of . If Q(5)=2, find P(5) and P(-5).

Answer 1

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Answer:

P(5) = 26

P(-5) = 6

Explanation:

The remainder statement tells us ...

P(x) = Q(x)·(x +5) +6

Evaluating this for x=5, we get ...

P(5) = Q(5)(5+5) +6

P(5) = (2)(10) +6

P(5) = 26

And for x = -5, we have ...

P(-5) = Q(-5)(-5 +5) +6

P(-5) = 0 +6

P(-5) = 6