Question

当 $x = 4$ 时，下面表达式的值是多少？ $\begin{aligned} &(3x - 2)(4x + 1) \\ &\quad {}- (3x - 2)4x + 1 \end{aligned}$

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

$0$

$1$

$10$

$11$

$12$

从前两项提出 $3x-2$ ，得 $\begin{aligned} &(3x - 2)\big[(4x + 1) - 4x\big] + 1 \\ &= (3x - 2)(1) + 1 \\ &= 3x - 1. \end{aligned}$

当 $x = 4$ 时，表达式等于 $3\cdot4 - 1 = 11$ 。

所以正确答案是 D。

Factoring $3x-2$ from the first two terms, $\begin{aligned} &(3x - 2)\big[(4x + 1) - 4x\big] + 1 \\ &= (3x - 2)(1) + 1 \\ &= 3x - 1. \end{aligned}$

At $x = 4,$ this equals $3\cdot4 - 1 = 11.$

Thus, the correct answer is D.