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Nonlinear Equations in One Variable and Systems of Equations

SAT Math· difficulty 4/5

When x3+4x2−x−4x^3 + 4x^2 - x - 4 is divided by x+4x + 4, the quotient is:

  • A

    x2−4x^2 - 4

  • B

    x2+4x−1x^2 + 4x - 1

  • C

    x2+1x^2 + 1

  • D

    x2−1x^2 - 1

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Explanation

Synthetic with −4-4: coefficients 1,4,−1,−41, 4, -1, -4. Bring down 1; 1(−4)=−41(-4) = -4, 4+(−4)=04 + (-4) = 0; 0(−4)=00(-4) = 0, −1+0=−1-1 + 0 = -1; −1(−4)=4-1(-4) = 4, −4+4=0-4 + 4 = 0. Quotient: x2+0x−1=x2−1x^2 + 0x - 1 = x^2 - 1.

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