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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]

To find the difference of the given polynomials, we'll proceed step-by-step:

We have two polynomials:

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

We need to subtract the second polynomial from the first one:

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

Now, let's distribute the negative sign to each term in the second polynomial:

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

Next, we'll combine like terms:

1. The [tex]\(x^3\)[/tex] term: [tex]\(5x^3\)[/tex] (no like terms to combine, it remains the same)
2. The [tex]\(x^2\)[/tex] terms: [tex]\(4x^2 - 6x^2 = -2x^2\)[/tex]
3. The [tex]\(x\)[/tex] term is [tex]\(2x\)[/tex] (no like terms to combine, it remains the same)
4. The constant term is [tex]\(9\)[/tex]

Putting it all together, the resulting polynomial is:

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

Therefore, the difference of the polynomials is:

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