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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+4x2+x−6p(x) = x^3 + 4x^2 + x - 6, find the other roots.

  • A

    x=−1,3x = -1, 3

  • B

    x=1,3x = 1, 3

  • C

    x=1,−3x = 1, -3

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  • D

    x=−1,−3x = -1, -3

Explanation

Divide by x+2x + 2: synthetic with −2-2, coefficients 1,4,1,−61, 4, 1, -6. Bring down 1; −2-2; 4+(−2)=24 + (-2) = 2; −4-4; 1+(−4)=−31 + (-4) = -3; 66; −6+6=0-6 + 6 = 0. Quotient: x2+2x−3=(x+3)(x−1)x^2 + 2x - 3 = (x+3)(x-1). Roots: 1,−31, -3.

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