How do you calculate the sum of the polynomials 4x³ + 2x² + 4x + 3 and 7x³ + 4x² + 7x + 8?

Finding the Sum of Polynomials

To find the sum of the polynomials 4x³ + 2x² + 4x + 3 and 7x³ + 4x² + 7x + 8, you need to combine like terms. This involves adding the coefficients of the terms that have the same degree.

Step 1: Identify Like Terms

Let’s break down both polynomials:

First Polynomial:
- 4x³
- 2x²
- 4x
- 3
Second Polynomial:
- 7x³
- 4x²
- 7x
- 8

Step 2: Add Like Terms

Now, we add the coefficients of the like terms:

x³ terms: 4x³ + 7x³ = (4 + 7)x³ = 11x³
x² terms: 2x² + 4x² = (2 + 4)x² = 6x²
x terms: 4x + 7x = (4 + 7)x = 11x
Constant terms: 3 + 8 = 11

Step 3: Combine the Results

Putting it all together, we get:

11x³ + 6x² + 11x + 11

Conclusion

The sum of the polynomials 4x³ + 2x² + 4x + 3 and 7x³ + 4x² + 7x + 8 is: