Math CentralQuandaries & Queries


Question from spencer, a student:

Hi im having a little bit of trouble with a question in polynomials 10 and was wondering if maybe someone could help
My question is 3x^3-3x-3 devided by 3x+6
If anyone could maybe help me out would be greatly appreciated :) thank you


I'm not sure of your question. Are you asked to divide 3x3 - 3x - 3 by 3x + 6 or are you asked if 3x3 - 3x - 3 is divisible by 3x + 6? I am going to assume you are asked if 3x3 - 3x - 3 is divisible by 3x + 6.

If 3x3 - 3x - 3 is divisible by 3x + 6 then there is a polynomial p(x) so that

(3x + 6) p(x) = 3x3 - 3x - 3.

You could find p(x) by long division if you wished, but in stead examine at the equation above. Each side is divisible by 3 so it simplifies to

(x + 2) p(x) = x3 - x - 1.

What is the value of the left side when x = -2?
What is the value of the right side when x = -2?


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