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Divide the polynomials.
The form of your answer should either be 
p(x) or 
p(x)+(k)/(x+3) where 
p(x) is a polynomial and 
k is an integer.

(2x^(3)-x^(2)-25 x-12)/(x+3)=

Divide the polynomials.\newlineThe form of your answer should either be p(x) p(x) or p(x)+kx+3 p(x)+\frac{k}{x+3} where p(x) p(x) is a polynomial and k k is an integer.\newline2x3x225x12x+3= \frac{2 x^{3}-x^{2}-25 x-12}{x+3}=

Full solution

Q. Divide the polynomials.\newlineThe form of your answer should either be p(x) p(x) or p(x)+kx+3 p(x)+\frac{k}{x+3} where p(x) p(x) is a polynomial and k k is an integer.\newline2x3x225x12x+3= \frac{2 x^{3}-x^{2}-25 x-12}{x+3}=
  1. Set up long division: Set up the long division.\newlineWe will use polynomial long division to divide (2x3x225x12)(2x^3 - x^2 - 25x - 12) by (x+3)(x + 3).
  2. Divide first term: Divide the first term of the dividend by the first term of the divisor.\newlineDivide 2x32x^3 by xx to get 2x22x^2.\newlineWrite 2x22x^2 above the division bar.
  3. Multiply divisor and result: Multiply the divisor (x+3)(x + 3) by the result from Step 22 (2x2)(2x^2).\newline2x2(x+3)=2x3+6x22x^2 * (x + 3) = 2x^3 + 6x^2.
  4. Subtract result from dividend: Subtract the result from Step 33 from the dividend.\newline(2x3x225x12)(2x3+6x2)=7x225x12(2x^3 - x^2 - 25x - 12) - (2x^3 + 6x^2) = -7x^2 - 25x - 12.
  5. Bring down next term: Bring down the next term of the dividend to prepare for the next division step.\newlineWe now have 7x225x-7x^2 - 25x.
  6. Divide first term of new dividend: Divide the first term of the new dividend by the first term of the divisor.\newlineDivide 7x2-7x^2 by xx to get 7x-7x.\newlineWrite 7x-7x above the division bar, next to 2x22x^2.
  7. Multiply divisor and result: Multiply the divisor (x+3)(x + 3) by the result from Step 66 (7x)(-7x).\newline7x×(x+3)=7x221x-7x \times (x + 3) = -7x^2 - 21x.
  8. Subtract result from new dividend: Subtract the result from Step 77 from the new dividend.\newline(7x225x)(7x221x)=4x(-7x^2 - 25x) - (-7x^2 - 21x) = -4x.
  9. Bring down next term: Bring down the next term of the dividend to prepare for the next division step.\newlineWe now have 4x12-4x - 12.
  10. Divide first term of new dividend: Divide the first term of the new dividend by the first term of the divisor.\newlineDivide 4x-4x by xx to get 4-4.\newlineWrite 4-4 above the division bar, next to 2x27x2x^2 - 7x.
  11. Multiply divisor and result: Multiply the divisor (x+3)(x + 3) by the result from Step 1010 (4)(-4).\newline4×(x+3)=4x12-4 \times (x + 3) = -4x - 12.
  12. Subtract result from new dividend: Subtract the result from Step 1111 from the new dividend.\newline(4x12)(4x12)=0(-4x - 12) - (-4x - 12) = 0.
  13. Write final answer: Write the final answer.\newlineSince there is no remainder, the result of the division is the polynomial written above the division bar: 2x27x42x^2 - 7x - 4.