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For the given polynomial P(x) and c = -4, use the remainder theorem to find P(c). P(x) = (2x^4 + 4x^2 + 7)...

For the given polynomial P(x) and c = -4, use the remainder theorem to find P(c).
P(x) = (2x^4 + 4x^2 + 7)
P(c) = (Simplify your answer. Type an integer or a fraction.)

Answer

To find P(c) using the remainder theorem, substitute c = -4 into the polynomial P(x):

  1. Calculate P(-4) = 2(-4)^4 + 4(-4)^2 + 7.
  2. First, compute (-4)^4 = 256 and (-4)^2 = 16.
  3. Then, P(-4) = 2(256) + 4(16) + 7 = 512 + 64 + 7 = 583.
  4. Therefore, P(c) = 583.

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