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Divide the polynomials.
Your answer should be a polynomial.

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

Divide the polynomials.\newlineYour answer should be a polynomial.\newlinex2+7x+10x+2= \frac{x^{2}+7 x+10}{x+2}=

Full solution

Q. Divide the polynomials.\newlineYour answer should be a polynomial.\newlinex2+7x+10x+2= \frac{x^{2}+7 x+10}{x+2}=
  1. Set up the division: Set up the division.\newlineWe are dividing the polynomial x2+7x+10x^2 + 7x + 10 by x+2x + 2. This is similar to long division with numbers. We will determine how many times x+2x + 2 goes into x2+7x+10x^2 + 7x + 10.
  2. Divide first term: Divide the first term of the dividend by the first term of the divisor. Divide x2x^2 by xx to get xx. This is the first term of the quotient.
  3. Multiply divisor and quotient: Multiply the divisor by the first term of the quotient.\newlineMultiply (x+2)(x + 2) by xx to get x2+2xx^2 + 2x. This will be subtracted from the dividend.
  4. Subtract result from dividend: Subtract the result from the dividend.\newlineSubtract (x2+2x)(x^2 + 2x) from (x2+7x+10)(x^2 + 7x + 10) to get 5x+105x + 10.
  5. Bring down next term: Bring down the next term of the dividend.\newlineSince we have already used x2x^2 and 7x7x, we bring down the next term, which is +10+10, to continue the division.
  6. Divide new term: Divide the new term of the dividend by the first term of the divisor. Divide 5x5x by xx to get 55. This is the next term of the quotient.
  7. Multiply divisor and new quotient: Multiply the divisor by the new term of the quotient. Multiply (x+2)(x + 2) by 55 to get 5x+105x + 10. This will be subtracted from the new dividend.
  8. Subtract result from new dividend: Subtract the result from the new dividend. Subtract 5x+105x + 10 from 5x+105x + 10 to get 00. This means the division is exact, and there is no remainder.