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Nonlinear Equations in One Variable and Systems of Equations

SAT Math· difficulty 4/5

If x+2x + 2 is a factor of p(x)=x3+ax2−4x+8p(x) = x^3 + ax^2 - 4x + 8, what is the value of aa?

  • A

    44

  • B

    22

  • C

    −2-2

    check_circle
  • D

    −4-4

Explanation

p(−2)=0p(-2) = 0: −8+4a+8+8=0⇒4a+8=0⇒a=−2-8 + 4a + 8 + 8 = 0 \Rightarrow 4a + 8 = 0 \Rightarrow a = -2.

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