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Divide. If there is a remainder, include it as a simplified fraction.\newline(h33h210h)÷(h+2)(h^3 - 3h^2 - 10h) \div (h + 2)\newline______

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Q. Divide. If there is a remainder, include it as a simplified fraction.\newline(h33h210h)÷(h+2)(h^3 - 3h^2 - 10h) \div (h + 2)\newline______
  1. Use Polynomial Long Division: To divide the polynomial (h33h210h)(h^3 - 3h^2 - 10h) by the binomial (h+2)(h + 2), we will use polynomial long division.
  2. Divide h3h^3 by hh: First, we divide the first term of the polynomial, h3h^3, by the first term of the binomial, hh, to get h2h^2.
  3. Multiply and Subtract: We then multiply the entire binomial (h+2)(h + 2) by h2h^2 and subtract the result from the polynomial.(h+2)×h2=h3+2h2(h + 2) \times h^2 = h^3 + 2h^2
  4. Subtract and Divide: Subtracting this from the original polynomial gives us:\newline(h33h210h)(h3+2h2)=5h210h(h^3 - 3h^2 - 10h) - (h^3 + 2h^2) = -5h^2 - 10h
  5. Multiply and Subtract: Next, we divide the first term of the new polynomial, 5h2-5h^2, by the first term of the binomial, hh, to get 5h-5h.
  6. Subtract and Complete: We then multiply the entire binomial (h+2)(h + 2) by 5h-5h and subtract the result from the new polynomial.(h+2)×5h=5h210h(h + 2) \times -5h = -5h^2 - 10h
  7. Subtract and Complete: We then multiply the entire binomial (h+2)(h + 2) by 5h-5h and subtract the result from the new polynomial.(h+2)×5h=5h210h(h + 2) \times -5h = -5h^2 - 10hSubtracting this from the new polynomial gives us:(5h210h)(5h210h)=0(-5h^2 - 10h) - (-5h^2 - 10h) = 0
  8. Subtract and Complete: We then multiply the entire binomial (h+2)(h + 2) by 5h-5h and subtract the result from the new polynomial.(h+2)5h=5h210h(h + 2) \cdot -5h = -5h^2 - 10hSubtracting this from the new polynomial gives us:(5h210h)(5h210h)=0(-5h^2 - 10h) - (-5h^2 - 10h) = 0Since we have no remainder, the division is complete.

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