SOLUTION: This problem is similar to another one I earlier but the answers are much different: Simplify: (3x^3 - 9x -3)/(3x +3) My answer: x^2 - x - 2, remainder 3 Problem is I have

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: This problem is similar to another one I earlier but the answers are much different: Simplify: (3x^3 - 9x -3)/(3x +3) My answer: x^2 - x - 2, remainder 3 Problem is I have      Log On


   



Question 172768: This problem is similar to another one I earlier but the answers are much different:
Simplify: (3x^3 - 9x -3)/(3x +3)
My answer: x^2 - x - 2, remainder 3
Problem is I have no idea where the x-2 is truly coming from. Is this correct and if so (or not) can someone please show me why?

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
Write it out like a regular long division problem, but remember to put in a place holder for the missing x%5E2 term in your dividend.

Divisor: 3x%2B3

Dividend: 3x%5E3+%2B+0x%5E2+-+9x+-+3

3x goes into 3x%5E3 x%5E2 times so x%5E2 becomes the first term in your quotient.

x%5E2 times 3 is 3x%5E2 so write that (with a plus sign in front of it) under the 0x%5E2 in your dividend. x%5E2 times 3x is 3x%5E3 so write that under the 3x%5E3 in your dividend.

Now subtract 3x%5E3%2B3x%5E2 from 3x%5E3%2B0x%5E2 (remember: change the sign and add) You should get -3x%5E2 -- write that at the bottom of your x%5E2 column.

Now bring down the next term -9x from the dividend and write that next to the result of your subtraction in the previous step. You should be looking at -3x%5E2-9x

3x goes into -3x%5E2-9x -x times, so -x becomes the next term in your quotient.

-x times 3x%2B3 is -3x%5E2-3x, subtraction results in -6x. Bring down the -3.

3x goes into -6x -2 times, so -2 becomes the third term in your quotient.

-2 times 3x%2B3 = -6x-6, subtraction results in %2B3.

3x does not go into 3 at all, so 3 is a remainder.

Putting the pieces of the quotient together you get: x%5E2-x-2 remainder 3.

Another way to express this would be %283x%5E3+-+9x+-3%29%2F%283x+%2B3%29=%28x%5E2-x-2%29%2B%283%2F%283x%2B3%29%29