Algebraically determine the values of h and k to correctly complete the identity stated below 3x^3-6x^2+4x-2 = (x-2) (3x^2+hx+4) + k

We want to find h and k so that

3x³ - 6x² + 4x - 2 ≡ (x-2) (3x² + hx + 4) + k

Expand the right side.

(x-2) (3x² + hx + 4) + k

= 3x³ + hx² + 4x - 6x² - 2hx - 8 + k

= 3x³ + (h-6) x² + (4 - 2h) x + k - 8

Match coefficients of x²:

h - 6 = - 6

h = 0

Match coefficients of x:

4 - 2h = 4 (Correct because h=0)

Match constants.

k - 8 = - 2

k = 6

Answer: h=0, k=6