Absolutely, let's do the polynomial subtraction step by step.
We have:
The first polynomial: 2 + 3x + 4x^2
The second polynomial: 2x^3 - 5x^2 - 5x + 2.
Subtracting polynomials is very similar to adding polynomials, but you need to distribute a "-1" throughout the second polynomial first before adding every term in the two polynomials. Here are the steps:
1. Distribute the "-1" throughout the second polynomial:
-2x^3 + 5x^2 + 5x - 2
2. Set up the problem for adding. Combine like terms, which are terms with the same degree in the variable:
(2 + 3x + 4x^2) + (-2x^3 + 5x^2 + 5x - 2)
= -2x^3 + 9x^2 + 8x
Hence, the difference between the two polynomials (2 + 3x + 4x^2) and (2x^3 - 5x^2 - 5x + 2) is -2x^3 + 9x^2 + 8x.