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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 :

To find the difference of the polynomials [tex]\((5x^3 + 4x^2) - (6x^2 - 2x - 9)\)[/tex], follow these steps:

1. Write down the first polynomial:
[tex]\[
5x^3 + 4x^2
\][/tex]

2. Write down the second polynomial (noticing the subtraction):
[tex]\[
(6x^2 - 2x - 9)
\][/tex]

3. Distribute the negative sign to each term in the second polynomial:
[tex]\[
-6x^2 + 2x + 9
\][/tex]

4. Combine the polynomials by adding the adjusted second polynomial to the first:
[tex]\[
(5x^3 + 4x^2) + (-6x^2 + 2x + 9)
\][/tex]

5. Now, combine like terms:
- The [tex]\(x^3\)[/tex] term: [tex]\(5x^3\)[/tex].
- The [tex]\(x^2\)[/tex] terms: [tex]\(4x^2 - 6x^2 = -2x^2\)[/tex].
- The [tex]\(x\)[/tex] term: [tex]\(2x\)[/tex].
- The constant term: [tex]\(9\)[/tex].

6. Put it all together:
[tex]\[
5x^3 - 2x^2 + 2x + 9
\][/tex]

So, the difference of the polynomials is:

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

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