Use the PRT (Polynomial Remainder Theorem) to determine the factors of polynomials and their remainders when divided by linear expressions.
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Problem

What is the remainder R when the polynomial p, left parenthesis, x, right parenthesis is divided by left parenthesis, x, plus, 1, right parenthesis, question mark
space, p, left parenthesis, x, right parenthesis, equals, 5, x, start superscript, 4, end superscript, plus, 6, x, start superscript, 3, end superscript, plus, x, start superscript, 2, end superscript, plus, 2, x, plus, 2
R, equals
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, p, i or 2, slash, 3, space, p, i
Is left parenthesis, x, plus, 1, right parenthesis a factor of p, left parenthesis, x, right parenthesis, question mark
Please choose from one of the following options.