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Nonlinear Equations in One Variable and Systems of Equations

SAT Math· difficulty 4/5

A polynomial p(x)p(x) leaves a remainder of 5 when divided by x−1x - 1 and 11 when divided by x−2x - 2. If p(x)=ax+bp(x) = ax + b, what are aa and bb?

  • A

    a=−6,b=11a = -6, b = 11

  • B

    a=6,b=1a = 6, b = 1

  • C

    a=6,b=−1a = 6, b = -1

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  • D

    a=5,b=0a = 5, b = 0

Explanation

p(1)=a+b=5p(1) = a + b = 5, p(2)=2a+b=11p(2) = 2a + b = 11. Subtract: a=6a = 6, b=−1b = -1.

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