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Divide the polynomials. The form of your answer should either be 
p(x) or 
p(x)+(k)/(x+1) where 
p(x) is a polynomial and 
k is an integer.

(3x^(3)+10x^(2)+7x)/(x+1)=

Divide the polynomials. The form of your answer should either be p(x) p(x) or p(x)+kx+1 p(x)+\frac{k}{x+1} where p(x) p(x) is a polynomial and k k is an integer.\newline3x3+10x2+7xx+1= \frac{3 x^{3}+10 x^{2}+7 x}{x+1}=

Full solution

Q. Divide the polynomials. The form of your answer should either be p(x) p(x) or p(x)+kx+1 p(x)+\frac{k}{x+1} where p(x) p(x) is a polynomial and k k is an integer.\newline3x3+10x2+7xx+1= \frac{3 x^{3}+10 x^{2}+7 x}{x+1}=
  1. Set up long division: Set up the long division.\newlineWe will use polynomial long division to divide 3x3+10x2+7x3x^3 + 10x^2 + 7x by x+1x + 1.
  2. Divide first term: Divide the first term of the dividend by the first term of the divisor.\newlineDivide 3x33x^3 by xx to get 3x23x^2. This will be the first term of the quotient.
  3. Multiply divisor and quotient: Multiply the divisor by the first term of the quotient.\newlineMultiply x+1x + 1 by 3x23x^2 to get 3x3+3x23x^3 + 3x^2.
  4. Subtract result from dividend: Subtract the result from the dividend.\newlineSubtract 3x3+3x23x^3 + 3x^2 from 3x3+10x23x^3 + 10x^2 to get 7x27x^2.
  5. Bring down next term: Bring down the next term of the dividend.\newlineBring down the +7x+7x term to get 7x2+7x7x^2 + 7x.
  6. Divide new first term: Divide the new first term of the dividend by the first term of the divisor.\newlineDivide 7x27x^2 by xx to get 7x7x. This will be the next term of the quotient.
  7. Multiply divisor and new term: Multiply the divisor by the new term of the quotient.\newlineMultiply x+1x + 1 by 7x7x to get 7x2+7x7x^2 + 7x.
  8. Subtract result from new dividend: Subtract the result from the new dividend.\newlineSubtract 7x2+7x7x^2 + 7x from 7x2+7x7x^2 + 7x to get 00.
  9. Division is complete: Since there is no remainder, the division is complete.\newlineThe quotient is 3x2+7x3x^2 + 7x, and there is no remainder.

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