Equivalent Expressions

SAT Math· difficulty 3/5

Which expression is equivalent to 2x2+7x+32x^2 + 7x + 3?

  • A

    (2x+1)(x+3)(2x + 1)(x + 3)

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  • B

    (2x+6)(x+0.5)(2x + 6)(x + 0.5)

  • C

    (2x1)(x3)(2x - 1)(x - 3)

  • D

    (2x+3)(x+1)(2x + 3)(x + 1)

Explanation

AC method: 23=62 \cdot 3 = 6; find two numbers multiplying to 6, summing to 7: 1 and 6. 2x2+x+6x+3=x(2x+1)+3(2x+1)=(2x+1)(x+3)2x^2 + x + 6x + 3 = x(2x+1) + 3(2x+1) = (2x+1)(x+3).

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