Q. Divide the polynomials. The form of your answer should either be p(x) or p(x)+x+1k where p(x) is a polynomial and k is an integer.x+13x3+10x2+7x=
Set up long division: Set up the long division.We will use polynomial long division to divide 3x3+10x2+7x by x+1.
Divide first term: Divide the first term of the dividend by the first term of the divisor.Divide 3x3 by x to get 3x2. This will be the first term of the quotient.
Multiply divisor and quotient: Multiply the divisor by the first term of the quotient.Multiply x+1 by 3x2 to get 3x3+3x2.
Subtract result from dividend: Subtract the result from the dividend.Subtract 3x3+3x2 from 3x3+10x2 to get 7x2.
Bring down next term: Bring down the next term of the dividend.Bring down the +7x term to get 7x2+7x.
Divide new first term: Divide the new first term of the dividend by the first term of the divisor.Divide 7x2 by x to get 7x. This will be the next term of the quotient.
Multiply divisor and new term: Multiply the divisor by the new term of the quotient.Multiply x+1 by 7x to get 7x2+7x.
Subtract result from new dividend: Subtract the result from the new dividend.Subtract 7x2+7x from 7x2+7x to get 0.
Division is complete: Since there is no remainder, the division is complete.The quotient is 3x2+7x, and there is no remainder.
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