Let's evaluate the expression [tex]\(\frac{3(x+4)(x+1)}{(x+2)(x-2)}\)[/tex] for [tex]\(x = 4\)[/tex].
1. Substitute [tex]\(x = 4\)[/tex] into each part of the expression:
[tex]\(\text{Numerator: } 3(x+4)(x+1)\)[/tex]
[tex]\[
3(4+4)(4+1)
\][/tex]
[tex]\(\text{Denominator: } (x+2)(x-2)\)[/tex]
[tex]\[
(4+2)(4-2)
\][/tex]
2. Simplify the expressions inside the parentheses:
[tex]\(\text{Numerator: } 3(8)(5)\)[/tex]
[tex]\[
3 \cdot 8 \cdot 5 = 120
\][/tex]
[tex]\(\text{Denominator: } 6 \cdot 2\)[/tex]
[tex]\[
6 \cdot 2 = 12
\][/tex]
3. Calculate the final result by dividing the numerator by the denominator:
[tex]\[
\frac{120}{12} = 10
\][/tex]
Therefore, the value of [tex]\(\frac{3(x+4)(x+1)}{(x+2)(x-2)}\)[/tex] for [tex]\(x=4\)[/tex] is [tex]\(10\)[/tex]. Thus, the correct answer is:
B. 10
