Polynomial p(x) when divided by x - 2 gives quotient x^2 + 3x + 1 and remainder 5. What is p(x)?

x^3 + x^2 - 5x + 3 p(x) = (x - 2)(x^2 + 3x + 1) + 5 = x^3 + 3x^2 + x - 2x^2 - 6x - 2 + 5 = x^3 + x^2 - 5x + 3.

Nonlinear Equations in One Variable and Systems of Equations

SAT Math· difficulty 5/5

p(x)

Explanation

p(x) = (x - 2)(x^2 + 3x + 1) + 5 = x^3 + 3x^2 + x - 2x^2 - 6x - 2 + 5 = x^3 + x^2 - 5x + 3

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