To find the perimeter of the triangle shown in the image, we need to add up the lengths of all three sides. The side lengths are expressed as algebraic expressions:

1. One side is $2x - 3$,
2. Another side is $2x^2 + 8x$,
3. The third side is $3x^2 - 6x + 5$.

The perimeter, $P$, is simply the sum of these three expressions:

$P = (2x - 3) + (2x^2 + 8x) + (3x^2 - 6x + 5)$

Now, combine like terms:

1. Combine the $x^2$ terms: $2x^2 + 3x^2 = 5x^2$,
2. Combine the $x$ terms: $2x + 8x - 6x = 4x$,
3. Combine the constant terms: $-3 + 5 = 2$.

So the perimeter expression is:

$P = 5x^2 + 4x + 2$

This is the expression for the perimeter of the triangle.

Would you like more details on any step, or do you have any questions?

Here are 5 follow-up questions to expand on this:

1. What happens to the perimeter if $x = 2$?
2. How can you interpret the perimeter if $x = 0$?
3. What is the degree of the polynomial that represents the perimeter?
4. How would you solve for $x$ if a specific perimeter value is given?
5. How does the coefficient of $x^2$ affect the shape of the triangle?

Tip: When adding algebraic expressions, always group and combine like terms to simplify the equation efficiently.