Question

I understand how to do i) , i dont understand how to do ii) for this : (x^3-8)/(x-2)

Answer 1

Have you considered using the hints?

You could just factor the numerator. Difference of Cubes, and all.

Answer 2

but i need to show the remainder theorem way , like the steps

Answer 3

using remainder means you replace x =2 (it comes from x-2 =0) into the numerator, what do you get is the remainder of the expression
2^3 -8 = 8-8=0, that means the numerator = denominator * something.

Answer 4

Synthetic Division demonstrating the Remainder Theorem