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Divide. If the polynomial does not divide evenly, include the remainder. (-2r^3 + 50r) ÷ (r - 5)

Divide. If the polynomial does not divide evenly, include the remainder.
(-2r^3 + 50r) ÷ (r - 5)

Answer

To divide the polynomial -2r^3 + 50r by r - 5, use polynomial long division:

  1. Divide the first term of the dividend (-2r^3) by the first term of the divisor (r), which gives -2r^2.
  2. Multiply the entire divisor (r - 5) by -2r^2, resulting in -2r^3 + 10r^2.
  3. Subtract this from the original polynomial: (-2r^3 + 50r) - (-2r^3 + 10r^2) = -10r^2 + 50r.
  4. Repeat the process: divide -10r^2 by r to get -10r.
  5. Multiply the divisor by -10r, resulting in -10r^2 + 50r.
  6. Subtract: (-10r^2 + 50r) - (-10r^2 + 50r) = 0.

The quotient is -2r^2 - 10r with a remainder of 0.

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