Q. Divide the polynomials.The form of your answer should either be p(x) or p(x)+x−5k where p(x) is a polynomial and k is an integer.x−52x3−11x2+25=
Set up long division: Set up the long division.We will use polynomial long division to divide (2x3−11x2+25) by (x−5).
Divide first term: Divide the first term of the numerator by the first term of the denominator.Divide 2x3 by x to get 2x2.Write 2x2 above the division bar.
Multiply divisor and result: Multiply the divisor (x−5) by the result from Step 2(2x2).2x2⋅(x−5)=2x3−10x2.Write this result under the corresponding terms of the dividend.
Subtract result from dividend: Subtract the result from Step 3 from the corresponding terms of the dividend.(2x3−11x2)−(2x3−10x2)=−x2.Bring down the next term of the dividend, which is +25.
Bring down next term: Divide the result from Step 4 by the first term of the divisor.Divide −x2 by x to get −x.Write −x above the division bar next to 2x2.
Divide result by first term: Multiply the divisor (x−5) by the result from Step 5(−x).−x×(x−5)=−x2+5x.Write this result under the corresponding terms of the dividend.
Multiply divisor and result: Subtract the result from Step 6 from the corresponding terms of the dividend.(−x2+25)−(−x2+5x)=−5x+25.
Subtract result from dividend: Divide the result from Step 7 by the first term of the divisor.Divide −5x by x to get −5.Write −5 above the division bar next to 2x2−x.
Divide result by first term: Multiply the divisor (x−5) by the result from Step 8(−5).−5×(x−5)=−5x+25.Write this result under the corresponding terms of the dividend.
Multiply divisor and result: Subtract the result from Step 9 from the corresponding terms of the dividend.(−5x+25)−(−5x+25)=0.There is no remainder, so the division is complete.
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