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.

Learn how to evaluate g(p+4) for the quadratic function g(x) = 3x^2 + 4x + 26 through a detailed step-by-step substitution process. This solution highlights key algebraic concepts such as expanding binomials and simplifying expressions. Suitable for high school students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation