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Nonlinear Equations in One Variable and Systems of Equations

SAT Math· difficulty 4/5

The polynomial p(x)=x3+kx2−3x+5p(x) = x^3 + kx^2 - 3x + 5 leaves a remainder of 7 when divided by x−1x - 1. What is the value of kk?

  • A

    −2-2

  • B

    −4-4

  • C

    44

    check_circle
  • D

    22

Explanation

p(1)=1+k−3+5=k+3=7p(1) = 1 + k - 3 + 5 = k + 3 = 7, so k=4k = 4.

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