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 will add the coefficients of the like terms separately.

Here are the steps:

1. Identify like terms: In both polynomials, we'll first identify the terms with the same variables raised to the same power. Here, we have terms with [tex]\(x^3\)[/tex] and terms with [tex]\(x^2\)[/tex].

2. Add coefficients of the [tex]\(x^3\)[/tex] terms:
- The first polynomial has a term [tex]\(7x^3\)[/tex].
- The second polynomial has a term [tex]\(2x^3\)[/tex].
- Add these coefficients together: [tex]\(7 + 2 = 9\)[/tex].
- So, the combined [tex]\(x^3\)[/tex] term is [tex]\(9x^3\)[/tex].

3. Add coefficients of the [tex]\(x^2\)[/tex] terms:
- The first polynomial has a term [tex]\(-4x^2\)[/tex].
- The second polynomial also has a term [tex]\(-4x^2\)[/tex].
- Add these coefficients: [tex]\(-4 + (-4) = -8\)[/tex].
- Thus, the combined [tex]\(x^2\)[/tex] term is [tex]\(-8x^2\)[/tex].

4. Write the resulting polynomial:
- Combine the results from the steps above: [tex]\(9x^3 - 8x^2\)[/tex].

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