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Answer :
We start with the expression
$$
(5x^3 + 4x^2) - (6x^2 - 2x - 9).
$$
The first step is to distribute the negative sign over the second polynomial:
$$
5x^3 + 4x^2 - 6x^2 + 2x + 9.
$$
Next, combine like terms. Notice that the terms $4x^2$ and $-6x^2$ are like terms:
$$
5x^3 + (4x^2 - 6x^2) + 2x + 9 = 5x^3 - 2x^2 + 2x + 9.
$$
Thus, the difference of the polynomials is
$$
5x^3 - 2x^2 + 2x + 9.
$$
This corresponds to option 4.
$$
(5x^3 + 4x^2) - (6x^2 - 2x - 9).
$$
The first step is to distribute the negative sign over the second polynomial:
$$
5x^3 + 4x^2 - 6x^2 + 2x + 9.
$$
Next, combine like terms. Notice that the terms $4x^2$ and $-6x^2$ are like terms:
$$
5x^3 + (4x^2 - 6x^2) + 2x + 9 = 5x^3 - 2x^2 + 2x + 9.
$$
Thus, the difference of the polynomials is
$$
5x^3 - 2x^2 + 2x + 9.
$$
This corresponds to option 4.
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