Question

Use the remainder theorem to find P(2) for P(x)=-x^3+3x^2+6.

Specifically, give the quotient and the remainder for the associated division and the value of P(2).

Answer 1

Answer: The value of P(2) is equal to 26

Explanation:

To find P(2) for the given polynomial P(x) = -x^3 + 3x^2 + 6, we can use the remainder theorem by dividing the polynomial by (x - 2).

-x^2 + 5x - 4

__________________________

x - 2 | -x^3 + 3x^2 + 0x + 6

(x^3 - 2x^2)

___________

5x^2 + 0x

(5x^2 - 10x)

____________

10x + 6

(10x - 20)

__________

26

The quotient is -x^2 + 5x - 4, and the remainder is 26.

Therefore, the value of P(2) is equal to the remainder, which is 26.