College

What is the sum of the polynomials?

[tex]\left(7x^3 - 4x^2\right) + \left(2x^3 - 4x^2\right)[/tex]

A. [tex]5x^3[/tex]

B. [tex]9x^3[/tex]

C. [tex]5x^3 - 8x^2[/tex]

D. [tex]9x^3 - 8x^2[/tex]

Answer :

To find the sum of the given polynomials [tex]\((7x^3 - 4x^2) + (2x^3 - 4x^2)\)[/tex], we need to combine like terms. Let's go through this step-by-step:

1. Identify the Like Terms:
- The terms involving [tex]\(x^3\)[/tex] are [tex]\(7x^3\)[/tex] and [tex]\(2x^3\)[/tex].
- The terms involving [tex]\(x^2\)[/tex] are [tex]\(-4x^2\)[/tex] and [tex]\(-4x^2\)[/tex].

2. Add the Coefficients of Like Terms:
- For the [tex]\(x^3\)[/tex] terms: Add the coefficients 7 and 2, which gives you [tex]\(9x^3\)[/tex].
- For the [tex]\(x^2\)[/tex] terms: Add the coefficients [tex]\(-4\)[/tex] and [tex]\(-4\)[/tex], which gives you [tex]\(-8x^2\)[/tex].

3. Write the Resulting Polynomial:
- Combine the results from the above additions to form the new polynomial: [tex]\(9x^3 - 8x^2\)[/tex].

Thus, the sum of the polynomials is [tex]\(9x^3 - 8x^2\)[/tex].