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Nonlinear Equations in One Variable and Systems of Equations

SAT Math· difficulty 5/5

A monic polynomial of degree 3 has roots 1,2,31, 2, 3. What is the polynomial expanded?

  • A

    x3−6x2+11x−6x^3 - 6x^2 + 11x - 6

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  • B

    x3−6x2−11x−6x^3 - 6x^2 - 11x - 6

  • C

    x3+6x2+11x+6x^3 + 6x^2 + 11x + 6

  • D

    x3−11x2+6x−6x^3 - 11x^2 + 6x - 6

Explanation

(x−1)(x−2)(x−3)(x-1)(x-2)(x-3). First (x−1)(x−2)=x2−3x+2(x-1)(x-2) = x^2 - 3x + 2. Then multiply by (x−3)(x-3): x3−3x2−3x2+9x+2x−6=x3−6x2+11x−6x^3 - 3x^2 - 3x^2 + 9x + 2x - 6 = x^3 - 6x^2 + 11x - 6.

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