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

2002 AMC 10B Problem 4

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What is the value of

\begin{aligned} &(3x - 2)(4x + 1) \\ &\quad {}- (3x - 2)4x + 1 \end{aligned}

when

x = 4?

0

1

10

11

12

Factor

3x - 2

out of the first two terms before plugging in

The bracket

(4x + 1) - 4x

collapses to

1

Factoring

3x-2

from the first two terms,

\begin{aligned} &(3x - 2)\big[(4x + 1) - 4x\big] + 1 \\ &= (3x - 2)(1) + 1 \\ &= 3x - 1. \end{aligned}

x = 4,

this equals

3\cdot4 - 1 = 11.

Thus, the correct answer is D.