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

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

• A. 4x3 + 4x2 + 5
• B. 2x3 + 2x2 + 5
• C. 3x3 + 5x2 + 10
• D. 5x3 + 2x - 5

Answer: (A)

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

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