Q. Divide the polynomials. Your answer should be a polynomial.x−5x2−3x−10=
Set up division format: Set up the division of the polynomials in long division format.We want to divide x2−3x−10 by x−5. This is similar to long division with numbers.
Divide first terms: Divide the first term of the dividend, x2, by the first term of the divisor, x, to get the first term of the quotient.x2÷x=x.Write x above the division bar.
Multiply and subtract: Multiply the divisor x−5 by the first term of the quotient x and write the result under the dividend.x×(x−5)=x2−5x.
Simplify and divide again: Subtract the result of the multiplication from the dividend.(x2−3x−10)−(x2−5x)=x2−3x−10−x2+5x.
Multiply and subtract again: Simplify the subtraction to find the new dividend.x2−3x−10−x2+5x=2x−10.
Simplify and find remainder: Divide the new dividend 2x−10 by the first term of the divisor x to find the next term of the quotient.2x÷x=2.Write 2 above the division bar next to the first term of the quotient.
Simplify and find remainder: Divide the new dividend 2x−10 by the first term of the divisor x to find the next term of the quotient.2x÷x=2.Write 2 above the division bar next to the first term of the quotient.Multiply the divisor x−5 by the new term of the quotient 2 and write the result under the new dividend.2×(x−5)=2x−10.
Simplify and find remainder: Divide the new dividend 2x−10 by the first term of the divisor x to find the next term of the quotient.2x÷x=2.Write 2 above the division bar next to the first term of the quotient.Multiply the divisor x−5 by the new term of the quotient 2 and write the result under the new dividend.2×(x−5)=2x−10.Subtract the result of the multiplication from the new dividend.(2x−10)−(2x−10)=2x−10−2x+10.
Simplify and find remainder: Divide the new dividend 2x−10 by the first term of the divisor x to find the next term of the quotient.2x÷x=2.Write 2 above the division bar next to the first term of the quotient.Multiply the divisor x−5 by the new term of the quotient 2 and write the result under the new dividend.2×(x−5)=2x−10.Subtract the result of the multiplication from the new dividend.(2x−10)−(2x−10)=2x−10−2x+10.Simplify the subtraction to find the remainder.2x−10−2x+10=0.The remainder is 0, so the division is exact.
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