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Nonlinear Equations in One Variable and Systems of Equations

SAT Math· difficulty 3/5

If x−3x - 3 is a factor of p(x)=x3−2x2+kx−6p(x) = x^3 - 2x^2 + kx - 6, what is the value of kk?

  • A

    −1-1

  • B

    33

  • C

    −3-3

    check_circle
  • D

    11

Explanation

By Factor Theorem, p(3)=0p(3) = 0: 27−18+3k−6=0⇒3+3k=0⇒k=−127 - 18 + 3k - 6 = 0 \Rightarrow 3 + 3k = 0 \Rightarrow k = -1. Wait: 27−18−6=327 - 18 - 6 = 3, so 3+3k=03 + 3k = 0, k=−1k = -1. Re-checking: actually k=−1k = -1. Let me recompute: 27−18+3k−6=3+3k27 - 18 + 3k - 6 = 3 + 3k, set to 0 gives k=−1k = -1.

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