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 polynomials [tex]\((7x^3 - 4x^2) + (2x^3 - 4x^2)\)[/tex], follow these steps:

1. Identify 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 [tex]\(x^3\)[/tex] Terms:
- Add the coefficients of the [tex]\(x^3\)[/tex] terms: [tex]\(7 + 2 = 9\)[/tex].
- So, the combined term for [tex]\(x^3\)[/tex] becomes [tex]\(9x^3\)[/tex].

3. Add the Coefficients of [tex]\(x^2\)[/tex] Terms:
- Add the coefficients of the [tex]\(x^2\)[/tex] terms: [tex]\((-4) + (-4) = -8\)[/tex].
- So, the combined term for [tex]\(x^2\)[/tex] becomes [tex]\(-8x^2\)[/tex].

4. Write the Resulting Polynomial:
- Combine the results from the previous steps to form the sum of the polynomials: [tex]\(9x^3 - 8x^2\)[/tex].

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