Question

Use the remainder theorem to find P(2) for P(x)=-x^4+4x^3-3x+3
Specifically, give the quotient and the remainder for the associated division and the value of P(2)

Answer 1

To find P(2) for the given polynomial P(x)=-x^4+4x^3-3x+3 using the remainder theorem, we must first divide the polynomial by (x-2), since we want to find P(2).

Performing the division, we get:

-2 | -1 4 0 -3 3
-2 -4 8 -10
----------------
-1 2 -4 7

Therefore, the quotient is -x^3+2x^2-4x+7 and the remainder is 7.

Now we can find P(2) by substituting x=2 into the polynomial:

P(2) = -(2)^4 + 4(2)^3 - 3(2) + 3
= -16 + 32 - 6 + 3
= 13

Therefore, P(2) = 13.