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Equivalent Expressions

SAT Math· difficulty 3/5

Which expression is equivalent to 3x2−11x−43x^2 - 11x - 4?

  • A

    (3x−4)(x+1)(3x - 4)(x + 1)

  • B

    (3x−1)(x+4)(3x - 1)(x + 4)

  • C

    (3x+1)(x−4)(3x + 1)(x - 4)

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  • D

    (3x+4)(x−1)(3x + 4)(x - 1)

Explanation

AC method: 3⋅(−4)=−123 \cdot (-4) = -12. Need numbers multiplying to −12-12, summing to −11-11: −12-12 and 11. 3x2−12x+x−4=3x(x−4)+1(x−4)=(3x+1)(x−4)3x^2 - 12x + x - 4 = 3x(x-4) + 1(x-4) = (3x+1)(x-4).

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