SOLUTION: I desperatly need help with this question on my final: Division of Polynomials. 2x-1 / 6x^3+x^2+0x+1

Question 116452: I desperatly need help with this question on my final: Division of Polynomials.
2x-1 / 6x^3+x^2+0x+1

Found 2 solutions by checkley71, slippinghalo3:
Answer by checkley71(8403) (Show Source): You can put this solution on YOUR website!
TRY DIVIDING (6X^3+X^2+0X+1) BY (2X-1) TO SEE IF IT IS A COMMON FACTOR.
THE DIVISION RESULTS ARE:
(2X-1)/(2X-1)(3X^2+2X-1) NOW YOU CAN CANCEL OUT THE (2X-1) TERMS.
1/(3X^2+2X-1) NO FACTOR THE DENOMINATOR.
1/(3X-1)(X+1) ANSWER.
Answer by slippinghalo3(3) (Show Source): You can put this solution on YOUR website!

The easiest way to solve this is to use long division. All you are doing is dividing except you have variables to worry about. For example 2x will go into 6x^3 3x^2 times, so write that at the top. 3x^2 * 2x = 6x^3 so put that beneath 6x^3. Then you need to take 3x^2 and multiply it by the second term (-1). You should get -3x^2. Now you will need to subtract both terms from the original terms. (6x^3 + x^2) - (6x^3 - 3x^2). DON'T FORGET TO DISTRIBUTE YOUR NEGATIVE! This should leave you with 4x^2. Now bring down your next term (0x) and repeat the process. 2x will go into 4x^2, 2x times. Put that at the top. 2x * 2x = 4x^2. 2x * -1 = -2x. (4x^2 + Ox) - (4x^2-2x) = 2x. Bring down your last term, so you have 2x-1. 2x goes into 2x 1 time (put that at the top). 1 * 2x = 2x. 1 * -1 = -1. Now you have (2x+1) - (2x-1). Leaving you with 2. Since you have no more terms to bring down 2 is your remainder. Write this as the remainder over the dividend, (2/(2x-1)). Your final answer will be 3x^2+2x+1+(2/(2x-1)).
I hope this makes sense to you. Good luck on your final. -Diana
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