SOLUTION: This is a long division problem that I'm having trouble with. I've tried to follow the book, but can't seem to solve it correctly....please help! Thank you. Perform the indicat

Question 44785: This is a long division problem that I'm having trouble with. I've tried to follow the book, but can't seem to solve it correctly....please help! Thank you.
Perform the indicated division...
(5n^4+28n^3-10n^2+196n-315)divided by (n^2+7)
Answer by aaaaaaaa(138) (Show Source): You can put this solution on YOUR website!
This will take some time because the polynomials are big, but I'll try to explain it. When long dividing two polynomials, you divide only the first term of the dividend for the first of the divisor (assuming the degrees are ordered from high to low, just like they are here: 4, 3, 2, 1, 0). Then you multiply the result by the whole polynomial, subtract, and repeat, until the degree of the dividend is lower than the degree of the divisor. This is best learned by example:

We'll divide first (always the terms with the highest exponent on both sides of the division). The quotient is We multiply and get . We then subtract the result from the dividend to get as our new dividend . Therefore:

Continuing:

Next step:

Fortunately, both terms cancel out and we have no remainder.

Therefore, summing up our quotients:

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