The legs of an isosceles triangle measures 2x^4+2x-1 units. The perimeter of the triangle is 5x^4-2x^3+x-3 units. Write a polynomial that represents the measure of the base of the triangle.

Perimeter = S1 + S2 + S3

5x^4-2x^3+x-3= (2x^4 + 2x-1) + (2x^4+2x-1) + base
5x^4-2x^3+x-3 = 2(2x^4 + 2x-1)+ base

5x^4-2x^3+x-3 - 2(2x^4 + 2x-1) = BASE
5x^4-2x^3+x-3 -4x^4-4x+2= BASE
5x^4-4x^4-2x^3-3x-1 = BASE

To find the measure of the base of the isosceles triangle, we need to set up an equation using the given information.

Let's denote the measure of the base of the triangle as "b" units. Since the triangle is isosceles, it means that the lengths of the two legs are equal.

Given that the lengths of the two legs are 2x^4 + 2x - 1 units, we can write the equation:

2(2x^4 + 2x - 1) + b = 5x^4 - 2x^3 + x - 3

First, distribute the 2 to the terms inside the parentheses:
4x^4 + 4x - 2 + b =5x^4 - 2x^3 + x - 3

Next, rearrange the equation by combining like terms:
4x^4 - 5x^4 - 2x^3 + 4x + x - b - 2 + 3 = 0

Combine the x^4 terms and the x^3 terms:
-x^4 - 2x^3 + 5x - b + 1 = 0

Finally, we can write the polynomial that represents the measure of the base of the triangle as:
-b - 2x^3 - x + x^4 + 1 = 0

So, the polynomial that represents the measure of the base of the isosceles triangle is -b - 2x^3 - x + x^4 + 1.