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Divide the polynomials.
The form of your answer should either be 
p(x) or 
p(x)+(k)/(x-4) where 
p(x) is a polynomial and 
k is an integer.

(4x^(3)-14x^(2)-7x-4)/(x-4)=

Divide the polynomials.\newlineThe form of your answer should either be p(x) p(x) or p(x)+kx4 p(x)+\frac{k}{x-4} where p(x) p(x) is a polynomial and k k is an integer.\newline4x314x27x4x4= \frac{4 x^{3}-14 x^{2}-7 x-4}{x-4}=

Full solution

Q. Divide the polynomials.\newlineThe form of your answer should either be p(x) p(x) or p(x)+kx4 p(x)+\frac{k}{x-4} where p(x) p(x) is a polynomial and k k is an integer.\newline4x314x27x4x4= \frac{4 x^{3}-14 x^{2}-7 x-4}{x-4}=
  1. Set up long division: Set up the long division.\newlineWe will use polynomial long division to divide 4x314x27x44x^3 - 14x^2 - 7x - 4 by x4x - 4.
  2. Divide first term of dividend: Divide the first term of the dividend by the first term of the divisor.\newlineDivide 4x34x^3 by xx to get 4x24x^2. Write 4x24x^2 above the dividend.
  3. Multiply divisor and subtract: Multiply the divisor by 4x24x^2 and subtract from the dividend.\newline4x2(x4)=4x316x24x^2 \cdot (x - 4) = 4x^3 - 16x^2. Subtract this from the dividend to get a new dividend of 2x27x4-2x^2 - 7x - 4.
  4. Divide first term of new dividend: Divide the first term of the new dividend by the first term of the divisor.\newlineDivide 2x2-2x^2 by xx to get 2x-2x. Write 2x-2x above the dividend next to 4x24x^2.
  5. Multiply divisor and subtract: Multiply the divisor by 2x-2x and subtract from the new dividend.\newline2x(x4)=2x2+8x-2x \cdot (x - 4) = -2x^2 + 8x. Subtract this from the new dividend to get a new dividend of 15x4-15x - 4.
  6. Divide first term of new dividend: Divide the first term of the new dividend by the first term of the divisor.\newlineDivide 15x-15x by xx to get 15-15. Write 15-15 above the dividend next to 2x-2x.
  7. Multiply divisor and subtract: Multiply the divisor by 15-15 and subtract from the new dividend.\newline15(x4)=15x+60-15 \cdot (x - 4) = -15x + 60. Subtract this from the new dividend to get a new dividend of 64-64.
  8. Check for further division: Since 64-64 is a constant and the divisor is linear, we cannot divide further. The remainder is 64-64.\newlineThe division process is complete, and the remainder is 64-64.

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