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Divide the polynomials.
Your answer should be a polynomial.

(x^(2)-8x+16)/(x-4)=

Divide the polynomials.\newlineYour answer should be a polynomial.\newlinex28x+16x4= \frac{x^{2}-8 x+16}{x-4}=

Full solution

Q. Divide the polynomials.\newlineYour answer should be a polynomial.\newlinex28x+16x4= \frac{x^{2}-8 x+16}{x-4}=
  1. Set up division: Set up the division of the polynomials in long division format.\newlineWe want to divide x28x+16x^2 - 8x + 16 by x4x - 4.
  2. Divide first terms: Divide the first term of the numerator by the first term of the denominator.\newlineDivide x2x^2 by xx to get xx.
  3. Multiply and subtract: Multiply the divisor (x4)(x - 4) by the result from Step 22 (x)(x) and write it below the dividend.\newlinex×(x4)=x24x.x \times (x - 4) = x^2 - 4x.
  4. Bring down next term: Subtract the result from Step 33 from the dividend.\newline(x28x+16)(x24x)=8x+4x+16=4x+16(x^2 - 8x + 16) - (x^2 - 4x) = -8x + 4x + 16 = -4x + 16.
  5. Repeat division process: Bring down the next term of the dividend if there is one.\newlineSince we have already brought down all terms, we proceed to the next step.
  6. Multiply and subtract: Repeat the division process with the new polynomial 4x+16-4x + 16.\newlineDivide 4x-4x by xx to get 4-4.
  7. Check remainder: Multiply the divisor (x4)(x - 4) by the result from Step 66 (4)(-4) and write it below the current dividend.\newline4×(x4)=4x+16-4 \times (x - 4) = -4x + 16.
  8. Division process complete: Subtract the result from Step 77 from the current dividend.\newline(4x+16)(4x+16)=0(-4x + 16) - (-4x + 16) = 0.
  9. Division process complete: Subtract the result from Step 77 from the current dividend.\newline(4x+16)(4x+16)=0(-4x + 16) - (-4x + 16) = 0.Since the remainder is 00, the division process is complete.\newlineThe quotient is the result from Step 22 and Step 66 combined, which is x4x - 4.