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Divide. If there is a remainder, include it as a simplified fraction.\newline(2x22x4)÷(x2)(2x^2 - 2x - 4) \div (x - 2)

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Q. Divide. If there is a remainder, include it as a simplified fraction.\newline(2x22x4)÷(x2)(2x^2 - 2x - 4) \div (x - 2)
  1. Set up division: Set up the division of the polynomial by the binomial.\newlineWe have: (2x22x4)÷(x2)(2x^2 - 2x - 4) \div (x - 2)\newlineWe will use polynomial long division to divide the terms.
  2. Divide first term: Divide the first term of the numerator by the first term of the denominator.\newlineDivide 2x22x^2 by xx to get 2x2x.\newlineWrite 2x2x above the division bar.
  3. Multiply and subtract: Multiply the divisor (x2)(x - 2) by the result from Step 22 (2x)(2x) and subtract from the original polynomial.(2x)(x2)=2x24x(2x)(x - 2) = 2x^2 - 4xSubtract this from the original polynomial:(2x22x4)(2x24x)=2x4(2x^2 - 2x - 4) - (2x^2 - 4x) = 2x - 4
  4. Bring down next term: Bring down the next term of the polynomial to continue the division.\newlineWe now have 2x42x - 4 remaining.
  5. 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.\text{Divide } 2x \text{ by } x \text{ to get } 2.Write 2 above the division bar next to 2x.\text{Write } 2 \text{ above the division bar next to } 2x.
  6. Multiply and subtract: Multiply the divisor (x2)(x - 2) by the result from Step 55 (2)(2) and subtract from the remaining polynomial.\newline(2)(x2)=2x4(2)(x - 2) = 2x - 4\newlineSubtract this from the remaining polynomial:\newline(2x4)(2x4)=0(2x - 4) - (2x - 4) = 0

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