To find $g(p+4)$, we will substitute $x = p+4$ into the function $g(x) = 3x^2 + 4x + 26$.

Steps:

1. Start with the function:
   $g(x) = 3x^2 + 4x + 26$

2. Substitute $x = p + 4$:
   $g(p+4) = 3(p+4)^2 + 4(p+4) + 26$

3. Expand the square $(p+4)^2$:
   $(p+4)^2 = p^2 + 8p + 16$ So,
   $g(p+4) = 3(p^2 + 8p + 16) + 4(p+4) + 26$

4. Distribute the 3 and the 4:
   $g(p+4) = 3p^2 + 24p + 48 + 4p + 16 + 26$

5. Combine like terms:
   $g(p+4) = 3p^2 + (24p + 4p) + (48 + 16 + 26)$ $g(p+4) = 3p^2 + 28p + 90$

So, the expression for $g(p+4)$ is: $g(p+4) = 3p^2 + 28p + 90$

Would you like more details or have any questions?

Here are some related questions to further explore:

1. What is $g(2)$ using the same function $g(x) = 3x^2 + 4x + 26$?
2. How would you solve $g(x) = 0$ for $x$?
3. Can you factor the expression $3p^2 + 28p + 90$?
4. How would you find the derivative of $g(x)$?
5. What happens if $g(x) = g(p+4)$? How would you solve for $x$?

Tip: When substituting variables into functions, always distribute and simplify carefully to avoid errors.