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Nonlinear Equations in One Variable and Systems of Equations

SAT Math· difficulty 4/5

Given that x=2x = 2 is a root of p(x)=x3−3x2−4x+12p(x) = x^3 - 3x^2 - 4x + 12, what are all the roots?

  • A

    x=−2,3,−3x = -2, 3, -3

  • B

    x=2,−2,3x = 2, -2, 3

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  • C

    x=2,3,−3x = 2, 3, -3

  • D

    x=2,−2,−3x = 2, -2, -3

Explanation

Divide by x−2x - 2: quotient is x2−x−6=(x−3)(x+2)x^2 - x - 6 = (x-3)(x+2). Roots: 2,3,−22, 3, -2.

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