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 polynomials [tex]\((7x^3 - 4x^2) + (2x^3 - 4x^2)\)[/tex], let's add the corresponding terms step by step:

1. Handle the [tex]\(x^3\)[/tex] terms:
- First polynomial has [tex]\(7x^3\)[/tex].
- Second polynomial has [tex]\(2x^3\)[/tex].
- Add these coefficients: [tex]\(7 + 2 = 9\)[/tex].

So, the [tex]\(x^3\)[/tex] term in the resulting polynomial is [tex]\(9x^3\)[/tex].

2. Handle the [tex]\(x^2\)[/tex] terms:
- First polynomial has [tex]\(-4x^2\)[/tex].
- Second polynomial has [tex]\(-4x^2\)[/tex].
- Add these coefficients: [tex]\(-4 + (-4) = -8\)[/tex].

So, the [tex]\(x^2\)[/tex] term in the resulting polynomial is [tex]\(-8x^2\)[/tex].

3. Combine the results:
- Combine the [tex]\(x^3\)[/tex] and [tex]\(x^2\)[/tex] terms 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].