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Divide the polynomials.
Your answer should be a polynomial.

(x^(2)-x-12)/(x+3)=◻

Divide the polynomials.\newlineYour answer should be a polynomial.\newlinex2x12x+3= \frac{x^{2}-x-12}{x+3}=

Full solution

Q. Divide the polynomials.\newlineYour answer should be a polynomial.\newlinex2x12x+3= \frac{x^{2}-x-12}{x+3}=
  1. Set up division format: Set up the division of the polynomials in long division format.\newlineWe want to divide x2x12x^2 - x - 12 by x+3x + 3.
  2. Divide first terms: Divide the first term of the dividend, x2x^2, by the first term of the divisor, xx, to get the first term of the quotient.\newlinex2x^2 divided by xx is xx.\newlineWrite xx above the division bar.
  3. Multiply and subtract: Multiply the divisor, x+3x + 3, by the first term of the quotient, xx, to get x(x+3)=x2+3xx(x + 3) = x^2 + 3x. Subtract this from the dividend under the division bar.
  4. Perform subtraction: Perform the subtraction step by subtracting (x2+3x)(x^2 + 3x) from (x2x)(x^2 - x).x2x(x2+3x)=x3x=4xx^2 - x - (x^2 + 3x) = -x - 3x = -4x. Bring down the next term of the dividend, which is 12-12, to get 4x12-4x - 12.
  5. Bring down next term: Divide the new first term of the remaining dividend, 4x-4x, by the first term of the divisor, xx, to get the next term of the quotient.\newline4x-4x divided by xx is 4-4.\newlineWrite 4-4 next to xx above the division bar, making the quotient x4x - 4.
  6. Divide new first term: Multiply the divisor, x+3x + 3, by the new term of the quotient, 4-4, to get 4(x+3)=4x12-4(x + 3) = -4x - 12. Subtract this from the remaining dividend under the division bar.
  7. Multiply and subtract: Perform the subtraction step by subtracting (4x12)(-4x - 12) from (4x12)(-4x - 12).\newline4x12(4x12)=0-4x - 12 - (-4x - 12) = 0.\newlineThere is no remainder, so the division is complete.