To add the two functions [tex]\( f(x) \)[/tex] and [tex]\( g(x) \)[/tex], we first need to look at their forms:
[tex]\[
f(x) = 3x^3 + 7x - 26
\][/tex]
[tex]\[
g(x) = x + 2
\][/tex]
Next, we will add them together:
[tex]\[
f(x) + g(x) = (3x^3 + 7x - 26) + (x + 2)
\][/tex]
Combine the like terms. Let's break this down step-by-step:
1. Identify and combine the [tex]\(x^3\)[/tex] terms:
[tex]\[
3x^3
\][/tex]
(No [tex]\(x^3\)[/tex] term from [tex]\(g(x)\)[/tex] to add)
2. Identify and combine the [tex]\(x\)[/tex] terms:
[tex]\[
7x + x = 8x
\][/tex]
3. Identify and combine the constant terms:
[tex]\[
-26 + 2 = -24
\][/tex]
Now, sum all the combined terms:
[tex]\[
3x^3 + 8x - 24
\][/tex]
Thus, the simplified polynomial form of [tex]\( h(x) \)[/tex] after adding [tex]\( f(x) \)[/tex] and [tex]\( g(x) \)[/tex] is:
[tex]\[
h(x) = 3x^3 + 8x - 24
\][/tex]
