Respuesta :

Solution:

  • Given,
  • [tex]p(x) = {7x}^{500} - {43x}^{56} - {3x}^{4} - 1[/tex]
  • Divisor =

[tex]x + 1[/tex]

  • By remainder theorem when p(x) is divided by x + 1, then remainder = p(-1). [Since, x+1=0 so, x = -1]
  • On putting x = -1 in p(x) we get

[tex]p( - 1) = 7( - 1)^{500} - {43( - 1)}^{56} - {3( - 1)}^{4} - 1 \\ = 7 - 43 - 3 - 1 \\ = - 40[/tex]

  • Remainder = -40

Answer:

The remainder is option 2. -40

Correct Option is -40

For explanation, please echeck the image attached.

By Benjemin

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