Q. Divide the polynomials.Your answer should be a polynomial.x−4x2−8x+16=
Set up division: Set up the division of the polynomials in long division format.We want to divide x2−8x+16 by x−4.
Divide first terms: Divide the first term of the numerator by the first term of the denominator.Divide x2 by x to get x.
Multiply and subtract: Multiply the divisor (x−4) by the result from Step 2(x) and write it below the dividend.x×(x−4)=x2−4x.
Bring down next term: Subtract the result from Step 3 from the dividend.(x2−8x+16)−(x2−4x)=−8x+4x+16=−4x+16.
Repeat division process: Bring down the next term of the dividend if there is one.Since we have already brought down all terms, we proceed to the next step.
Multiply and subtract: Repeat the division process with the new polynomial −4x+16.Divide −4x by x to get −4.
Check remainder: Multiply the divisor (x−4) by the result from Step 6(−4) and write it below the current dividend.−4×(x−4)=−4x+16.
Division process complete: Subtract the result from Step 7 from the current dividend.(−4x+16)−(−4x+16)=0.
Division process complete: Subtract the result from Step 7 from the current dividend.(−4x+16)−(−4x+16)=0.Since the remainder is 0, the division process is complete.The quotient is the result from Step 2 and Step 6 combined, which is x−4.
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