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Answer :
To find the difference of the polynomials [tex]\((5x^3 + 4x^2) - (6x^2 - 2x - 9)\)[/tex], we can follow these steps:
1. Rewrite the Expression:
We start by distributing the negative sign to the second polynomial. This changes the subtraction into an addition of the additive inverse:
[tex]\[
5x^3 + 4x^2 - (6x^2 - 2x - 9) = 5x^3 + 4x^2 - 6x^2 + 2x + 9
\][/tex]
2. Combine Like Terms:
Now, we combine like terms:
- Cubic terms: There is only one cubic term, [tex]\(5x^3\)[/tex].
- Quadratic terms: [tex]\(4x^2 - 6x^2 = -2x^2\)[/tex].
- Linear terms: The only linear term is [tex]\(2x\)[/tex].
- Constant terms: The constant term is [tex]\(+9\)[/tex].
Thus, the expression becomes:
[tex]\[
5x^3 - 2x^2 + 2x + 9
\][/tex]
The difference of the polynomials is:
[tex]\[
5x^3 - 2x^2 + 2x + 9
\][/tex]
This matches the third option from the given list.
1. Rewrite the Expression:
We start by distributing the negative sign to the second polynomial. This changes the subtraction into an addition of the additive inverse:
[tex]\[
5x^3 + 4x^2 - (6x^2 - 2x - 9) = 5x^3 + 4x^2 - 6x^2 + 2x + 9
\][/tex]
2. Combine Like Terms:
Now, we combine like terms:
- Cubic terms: There is only one cubic term, [tex]\(5x^3\)[/tex].
- Quadratic terms: [tex]\(4x^2 - 6x^2 = -2x^2\)[/tex].
- Linear terms: The only linear term is [tex]\(2x\)[/tex].
- Constant terms: The constant term is [tex]\(+9\)[/tex].
Thus, the expression becomes:
[tex]\[
5x^3 - 2x^2 + 2x + 9
\][/tex]
The difference of the polynomials is:
[tex]\[
5x^3 - 2x^2 + 2x + 9
\][/tex]
This matches the third option from the given list.
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