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2002 AMC 12B Problem 2

Problem 2 of 25EasierAlgebra

What is the value of (3x−2)(4x+1)−(3x−2)4x+1 \begin{aligned} &(3x-2)(4x+1) \\ &\quad {}-(3x-2)4x+1 \end{aligned} when x=4?x=4?

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Solution

Factor 3x−23x-2 out of the first two terms: (3x−2)(4x+1)−(3x−2)4x+1=(3x−2)(4x+1−4x)+1=3x−1. \begin{gathered} (3x-2)(4x+1) \\ {}-(3x-2)4x+1 \\ {}=(3x-2)(4x+1-4x)+1 \\ {}=3x-1. \end{gathered} At x=4x=4 this equals 3⋅4−1=11.3\cdot4-1=11. Thus, the correct answer is D.

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Concepts: algebraic manipulation · factoring

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.