Q. Divide. If there is a remainder, include it as a simplified fraction.(2x2−2x−4)÷(x−2)
Set up division: Set up the division of the polynomial by the binomial.We have: (2x2−2x−4)÷(x−2)We will use polynomial long division to divide the terms.
Divide first term: Divide the first term of the numerator by the first term of the denominator.Divide 2x2 by x to get 2x.Write 2x above the division bar.
Multiply and subtract: Multiply the divisor (x−2) by the result from Step 2(2x) and subtract from the original polynomial.(2x)(x−2)=2x2−4xSubtract this from the original polynomial:(2x2−2x−4)−(2x2−4x)=2x−4
Bring down next term: Bring down the next term of the polynomial to continue the division.We now have 2x−4 remaining.
Divide new first term: Divide the new first term of the remaining polynomial by the first term of the divisor.Divide 2x by x to get 2.Write 2 above the division bar next to 2x.
Multiply and subtract: Multiply the divisor (x−2) by the result from Step 5(2) and subtract from the remaining polynomial.(2)(x−2)=2x−4Subtract this from the remaining polynomial:(2x−4)−(2x−4)=0
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