College

What is the difference of the polynomials?

[tex]\left(5x^3 + 4x^2\right) - \left(6x^2 - 2x - 9\right)[/tex]

A. [tex]-x^3 + 6x^2 + 9[/tex]

B. [tex]-x^3 + 2x^2 - 9[/tex]

C. [tex]5x^3 - 2x^2 - 2x - 9[/tex]

D. [tex]5x^3 - 2x^2 + 2x + 9[/tex]

Answer :

We are given the expression

[tex]$$\left(5x^3 + 4x^2\right) - \left(6x^2 - 2x - 9\right).$$[/tex]

Step 1: Remove the Parentheses

Distribute the minus sign across the second polynomial:

[tex]$$
5x^3 + 4x^2 - 6x^2 + 2x + 9.
$$[/tex]

Step 2: Combine Like Terms

Group the like terms together:

- The [tex]$x^3$[/tex] term remains: [tex]$$5x^3.$$[/tex]
- Combine the [tex]$x^2$[/tex] terms: [tex]$$4x^2 - 6x^2 = -2x^2.$$[/tex]
- The [tex]$x$[/tex] term is: [tex]$$+ 2x.$$[/tex]
- The constant term is: [tex]$$+ 9.$$[/tex]

So, the simplified expression becomes:

[tex]$$
5x^3 - 2x^2 + 2x + 9.
$$[/tex]

Final Answer

The difference of the polynomials is

[tex]$$\boxed{5x^3 - 2x^2 + 2x + 9}.$$[/tex]