Q. Divide the polynomials.Your answer should be a polynomial.x−10x2−12x+20=
Set up division: Set up the division of the polynomials in long division format.We want to divide (x2−12x+20) by (x−10).
Divide first term: Divide the first term of the numerator by the first term of the denominator.Divide x2 by x to get x.
Multiply and write: Multiply the divisor (x−10) by the result from Step 2(x) and write it under the dividend.x×(x−10)=x2−10x.
Subtract and simplify: Subtract the result from Step 3 from the dividend.(x2−12x+20)−(x2−10x)=−12x+20−(−10x)=−12x+20+10x=−2x+20.
Bring down next term: 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.
Divide new first term: Divide the new first term of the remaining dividend by the first term of the divisor.Divide −2x by x to get −2.
Multiply and write: Multiply the divisor (x−10) by the result from Step 6(−2) and write it under the remaining dividend.−2×(x−10)=−2x+20.
Subtract and simplify: Subtract the result from Step 7 from the remaining dividend.(−2x+20)−(−2x+20)=0.
Check for remainder: Since the remainder is 0, the division is complete, and the quotient is the final answer.The quotient is x−2.
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