2002 AMC 12B Problem 2

Below is the professionally curated solution for Problem 2 of the 2002 AMC 12B, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2002 AMC 12B solutions, or check the answer key.

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Concepts:algebraic manipulationfactoring

Difficulty rating: 980

2.

What is the value of (3x2)(4x+1)(3x2)4x+1(3x-2)(4x+1)-(3x-2)4x+1 when x=4?x=4?

00

11

1010

1111

1212

Solution:

Factor 3x23x-2 out of the first two terms: (3x2)(4x+1)(3x2)4x+1=(3x2)(4x+14x)+1=3x1.(3x-2)(4x+1)-(3x-2)4x+1=(3x-2)(4x+1-4x)+1=3x-1. At x=4x=4 this equals 341=11.3\cdot4-1=11.

Thus, the correct answer is D.

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