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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 want to simplify

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

Step 1. Remove Parentheses

First, distribute the minus sign to each term in the second polynomial:

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

Step 2. Combine Like Terms

Next, group and combine the like terms:

- The term with [tex]$x^3$[/tex] is [tex]$5x^3$[/tex].
- For the [tex]$x^2$[/tex] terms, combine [tex]$4x^2$[/tex] and [tex]$-6x^2$[/tex]:
[tex]\[
4x^2 - 6x^2 = -2x^2.
\][/tex]
- The term with [tex]$x$[/tex] is [tex]$2x$[/tex].
- The constant term is [tex]$9$[/tex].

So, putting everything together, we have

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

Step 3. Final Answer

Thus, the difference of the polynomials is

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

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