Let's find \( P(x) + Q(x) \) step-by-step given the functions \( P(x) \) and \( Q(x) \) defined as:
[tex]\[ P(x) = 6x \][/tex]
[tex]\[ Q(x) = 2x^3 + 3x^2 + 1 \][/tex]
To find \( P(x) + Q(x) \), we simply need to add these two functions together:
[tex]\[ P(x) + Q(x) = 6x + (2x^3 + 3x^2 + 1) \][/tex]
Now, let's combine like terms:
[tex]\[ P(x) + Q(x) = 2x^3 + 3x^2 + 6x + 1 \][/tex]
Our resulting expression for \( P(x) + Q(x) \) is:
[tex]\[ 2x^3 + 3x^2 + 6x + 1 \][/tex]
Next, let's compare this result with the given choices:
A. \( 11x^6 + 1 \)
B. \( 2x^3 + 3x^2 + 6x + 1 \)
C. \( 8x^4 + 3x^2 + 1 \)
Clearly, the correct answer matches choice B:
[tex]\[ 2x^3 + 3x^2 + 6x + 1 \][/tex]
Therefore, the correct choice is:
[tex]\[ \boxed{B} \][/tex]
