SOLUTION: I know that this seems extremly simple by simply dividing but for some reason I am having great difficulty when trying to divide these polynomials. I truly would appreciate your he

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Question 243193: I know that this seems extremly simple by simply dividing but for some reason I am having great difficulty when trying to divide these polynomials. I truly would appreciate your help as I have been working on two problems for the past 3 hours and none of the answers I have seem correct in the least when compared to the practice questions that are similar which I can not get right either. Thanks again!!
(5x(to the seventh power) - 3x (to the fourth power) + 2x(squared)- 10x +2) / (x (squared) -x + 1)
Answer by oberobic(2304) (Show Source):
You can put this solution on YOUR website!
The keys to polynomial division are to keep everything in alignment and to remember to add the missing factors into the equation with coefficient 0. In this case you are asked to do the following division.

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Setting up the division on a clean sheet of paper, you simply start dividing just like you've done with other polynomials. You determine what 5x^7 divided x^2 will yield. In this case it is 5x^5. Then multiply the whole divisor by 5x^5. That equals 5x^7 - 5x^6 + 5x^5. Place these directly under the columns with the same exponents and subtract.
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Continue in this way until you get to the end. I have solved the problem but do not have the means to show the long division here. But I can give you the answer:
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It would have been lovely if the original dividend had ended with +12 instead of +2. If it had been +12, then the polynomial division would have come out even. However, we ended up with a remainder of -10. So you have to append that to the quotient with its divisor, as shown.
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Check your work by multiplying it back out.