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Nonlinear Equations in One Variable and Systems of Equations

SAT Math· difficulty 4/5

Find all real solutions of x3+x2−4x−4=0x^3 + x^2 - 4x - 4 = 0.

  • A

    x=1,−2,2x = 1, -2, 2

  • B

    x=−1,−2,−4x = -1, -2, -4

  • C

    x=−1,2,−2x = -1, 2, -2

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  • D

    x=1,4x = 1, 4

Explanation

Group: x2(x+1)−4(x+1)=(x+1)(x2−4)=(x+1)(x−2)(x+2)=0x^2(x+1) - 4(x+1) = (x+1)(x^2 - 4) = (x+1)(x-2)(x+2) = 0. Solutions: −1,2,−2-1, 2, -2.

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