Sure, let's solve the equation step by step to find the missing expression.
We start with the equation given:
[tex]\[ x^8 + 3 x^5 = x^5 \cdot \text{(missing expression)} \][/tex]
Our goal is to determine the missing expression on the right-hand side.
First, we can factor out [tex]\( x^5 \)[/tex] from the left-hand side of the equation:
[tex]\[ x^8 + 3 x^5 = x^5 (x^3) + x^5 (3) \][/tex]
When we factor [tex]\( x^5 \)[/tex] out of the terms on the left, the equation becomes:
[tex]\[ x^8 + 3 x^5 = x^5 (x^3 + 3) \][/tex]
So, the missing expression in the given equation is:
[tex]\[ \boxed{x^3 + 3} \][/tex]
Therefore, the complete equation is:
[tex]\[ x^8 + 3 x^5 = x^5 (x^3 + 3) \][/tex]
This verifies that our missing expression is indeed [tex]\( x^3 + 3 \)[/tex].
