SOLUTION: Ok-I am working on Division of polynomials vs monomials. But the book does not show me how to work out (((x cubed minus 8 divided by x minus 2))). The long division is not working

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Question 148988This question is from textbook Introduction to Technical Mathematics
: Ok-I am working on Division of polynomials vs monomials. But the book does not show me how to work out (((x cubed minus 8 divided by x minus 2))). The long division is not working for me. I cannot figure out who to divide this problem to get an appropriate or correct answer. This question is from textbook Introduction to Technical Mathematics

Answer by mangopeeler07(462) About Me  (Show Source):
You can put this solution on YOUR website!
difference of cubes= a^3-b^3
a^3-b^3=(a-b)(a^2+ab+b^2)

in x^3-8, a=cube root of x^3 (or x) and b=cube root of 8 (or 2)
plug those in for a and b

So x^3-8/x-2 becomes
(x-2)(x^2+2x+4)/(x-2)

Now cancel the x-2 expressions and get
%28x%5E2%2B2x%2B4%29

This is the answer, but if you wish to factor it, you get:
%28x%2B2%29%5E2-2x
since %28x%2B2%29%5E2=x%5E2%2B4x%2B4
subtract 2x and get x%5E2%2B2x%2B4