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], you need to follow these steps:

1. Identify Like Terms: Look for terms in each polynomial that have the same degree. In this case, the like terms are the terms involving [tex]\(x^3\)[/tex] and the terms involving [tex]\(x^2\)[/tex].

2. Combine Like Terms for [tex]\(x^3\)[/tex]:
- From the first polynomial, [tex]\((7x^3 - 4x^2)\)[/tex], the term is [tex]\(7x^3\)[/tex].
- From the second polynomial, [tex]\((2x^3 - 4x^2)\)[/tex], the term is [tex]\(2x^3\)[/tex].
- Add these terms together: [tex]\(7x^3 + 2x^3 = 9x^3\)[/tex].

3. Combine Like Terms for [tex]\(x^2\)[/tex]:
- From the first polynomial, the term for [tex]\(x^2\)[/tex] is [tex]\(-4x^2\)[/tex].
- From the second polynomial, the term for [tex]\(x^2\)[/tex] is also [tex]\(-4x^2\)[/tex].
- Add these terms together: [tex]\(-4x^2 + (-4x^2) = -8x^2\)[/tex].

4. Write the Resulting Polynomial: After combining the like terms, the sum of the polynomials is [tex]\(9x^3 - 8x^2\)[/tex].

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