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Nonlinear Equations in One Variable and Systems of Equations

SAT Math· difficulty 4/5

What is the quotient when x3−2x2−5x+6x^3 - 2x^2 - 5x + 6 is divided by x−1x - 1?

  • A

    x2+x−6x^2 + x - 6

  • B

    x2−x+6x^2 - x + 6

  • C

    x2−2x−5x^2 - 2x - 5

  • D

    x2−x−6x^2 - x - 6

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Explanation

Synthetic division with 1: coefficients 1,−2,−5,61, -2, -5, 6. Bring down 1, 1⋅1=11 \cdot 1 = 1, −2+1=−1-2+1 = -1; −1⋅1=−1-1 \cdot 1 = -1, −5+(−1)=−6-5 + (-1) = -6; −6⋅1=−6-6 \cdot 1 = -6, 6+(−6)=06 + (-6) = 0. Quotient: x2−x−6x^2 - x - 6.

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