Sure, let's analyze and simplify the given algebraic expression step-by-step.
Given expression:
[tex]\[ v^2 + 2v + 15 \][/tex]
### Step 1: Identify the structure of the expression
The given expression is a quadratic expression in the variable [tex]\( v \)[/tex]. A general quadratic expression is of the form:
[tex]\[ ax^2 + bx + c \][/tex]
In this case:
- [tex]\( a = 1 \)[/tex]
- [tex]\( b = 2 \)[/tex]
- [tex]\( c = 15 \)[/tex]
### Step 2: Expand (if needed) and combine like terms
In our expression [tex]\( v^2 + 2v + 15 \)[/tex], all the terms are already combined as much as they can be. So, we really just have to recognize and interpret it as is.
### Step 3: Solutions or further simplifications
If we were asked to factor the given expression, we would look for factors of [tex]\( v^2 + 2v + 15 \)[/tex]. Since [tex]\( v^2+2v+15 \)[/tex] does not factor nicely into real numbers due to the constant 15 not having pairs of factorable terms that sum up to 2 in the linear term, we might stop there or use the quadratic formula to find any roots, but:
Given the original problem didn't ask specifically for factoring or solving for [tex]\( v \)[/tex], we consider the expression given [tex]\( v^2 + 2v + 15 \)[/tex] as our simplified form.
Thus, the analyzed and confirmed expression is:
[tex]\[ v^2 + 2v + 15 \][/tex]
This is a quadratic polynomial with no further simple factorization available using real numbers. The expression represents a parabola that opens upwards due to the positive coefficient of [tex]\( v^2 \)[/tex].
