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Nonlinear Equations in One Variable and Systems of Equations

SAT Math· difficulty 5/5

For which value of aa is x−3x - 3 a factor of p(x)=x3−5x2+ax+12p(x) = x^3 - 5x^2 + ax + 12?

  • A

    a=−2a = -2

  • B

    a=2a = 2

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  • C

    a=0a = 0

  • D

    a=−4a = -4

Explanation

p(3)=27−45+3a+12=−6+3a=0⇒a=2p(3) = 27 - 45 + 3a + 12 = -6 + 3a = 0 \Rightarrow a = 2.

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