What is the sum of 3x3 - 2x + 8, 2x2 + 5x, and x3 + 2x2 - 3x - 3?

To find the sum of the given polynomials, we need to combine the like terms from each expression.

Starting with the three polynomials:

1. (3x^3 - 2x + 8)

2. (2x^2 + 5x)

3. (x^3 + 2x^2 - 3x - 3)

Now, let's group the terms based on their degrees:

• Cubic terms: (3x^3) from the first polynomial and (x^3) from the third polynomial combine to give (3x^3 + x^3 = 4x^3).

• Quadratic terms: (2x^2) from the second polynomial and (2x^2) from the third polynomial add up to (2x^2 + 2x^2 = 4x^2).

• Linear terms: The first polynomial contributes (-2x), the second one contributes (5x), and the third polynomial contributes (-3x). Combining these gives (-2x + 5x - 3x = 0x), meaning the linear terms