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Nonlinear Equations in One Variable and Systems of Equations

SAT Math· difficulty 5/5

The polynomial p(x)=2x3−x2+ax+bp(x) = 2x^3 - x^2 + ax + b has x−1x - 1 as a factor and p(0)=−3p(0) = -3. What is the value of aa?

  • A

    00

  • B

    −2-2

  • C

    22

    check_circle
  • D

    33

Explanation

p(0)=b=−3p(0) = b = -3. p(1)=2−1+a+b=1+a−3=a−2=0⇒a=2p(1) = 2 - 1 + a + b = 1 + a - 3 = a - 2 = 0 \Rightarrow a = 2.

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