High School

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], follow these steps:

1. Identify the Like Terms:
- Look at the terms in each polynomial:
- The first polynomial is [tex]\(7x^3 - 4x^2\)[/tex].
- The second polynomial is [tex]\(2x^3 - 4x^2\)[/tex].

2. Combine the Coefficients of Like Terms:
- For the [tex]\(x^3\)[/tex] terms:
- Add the coefficients: [tex]\(7 + 2 = 9\)[/tex].
- So, the result for the [tex]\(x^3\)[/tex] terms is [tex]\(9x^3\)[/tex].
- For the [tex]\(x^2\)[/tex] terms:
- Add the coefficients: [tex]\(-4 + (-4) = -8\)[/tex].
- So, the result for the [tex]\(x^2\)[/tex] terms is [tex]\(-8x^2\)[/tex].

3. Write the Resulting Polynomial:
- Combine the results from the like terms: [tex]\(9x^3 - 8x^2\)[/tex].

Therefore, the sum of the polynomials is [tex]\(9x^3 - 8x^2\)[/tex]. This matches the option [tex]\(9x^3 - 8x^2\)[/tex] from the choices provided.