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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 the expression

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

**Step 1. Distribute the negative sign**

When subtracting the polynomial inside the parentheses, distribute the negative sign to each term:

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

**Step 2. Combine like terms**

Now, group and combine like terms:

- The term $5x^3$ has no like term.
- Combine the $x^2$ terms: $4x^2 - 6x^2 = -2x^2$.
- The $x$ term is $2x$, and the constant term is $9$.

So the expression becomes:

$$
5x^3 - 2x^2 + 2x + 9.
$$

Thus, the difference of the polynomials is

$$
\boxed{5x^3 - 2x^2 + 2x + 9}.
$$

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