Question

Express the polynomial below in the form P(x) = (x - k) times the quotient plus the remainder for the given value of k. P(x) = 3x3 - x2 + 2x + 7; k = -1

Answer 1

P(x) = (3x^2 + -4x + 6)(x +1 ) + ( 1 )/( x + 1)

Explanation:

First we have to divide the polynomial

3x^3 - x^2 + 2x + 7 | x+1

-3x^3 - 3x^2 3x^2 - 4x +6

-4x^2 +2x +7

4x^2 +4x

6x + 7

-6x - 6

1

Hence we have

P(x)=(x-k)Q(x) + R(x) = (x-k)Q(x) + 1/(x-k)

P(x) = 3x^3 - x^2 + 7 = (3x^2 + -4x + 6)(x +1 ) + ( 1 )/( x + 1)

HOPE THIS HELPS!!

Answer 2

Answer: ( X- k )(3x2 - 4x + 7) + 1

Step-by-step explanation: Please find the attached files for the solution