SOLUTION: for problem use the Remaider Theorem to find P(c) P(x)=5x^3-4x^2+x-7, c=3

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Question 239325: for problem use the Remaider Theorem to find P(c)
P(x)=5x^3-4x^2+x-7, c=3
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
The Remainder Theorem tells us that if some polynomial P(x) is divided by (x-c) then
P(x) = Q(x)(x-c) + R
where Q(x) is the quotient and R is the remainder of the division. Then
P(c) = Q(c)((c)-c) + R
Since (c-c) = 0 it will not matter what Q(c) is because when you multiply whatever Q(c) is by 0 you will get 0. And since 0+R = R, P(c) = R.

So we can find P(c) by using the remainder of dividing P(x) by (x-c). In your problem c = 3 so we will divide by (x-3) (using Synthetic Division):
3 |   5   -4   1   -7
---       15  33  102
     ----------------
      5   11  34   95

So P(3) = 95.

(You should get the same answer if you use Long Division instead of Synthetic Division.)