College

What is the difference of the polynomials?

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

Sure! Let's find the difference between the given polynomials 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:

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

To do this, we distribute the negative sign through the second polynomial:

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

Now, let's combine like terms:

- The cubic term is [tex]\( 5x^3 \)[/tex].
- For the quadratic terms, combine: [tex]\( 4x^2 - 6x^2 = -2x^2 \)[/tex].
- The linear term is [tex]\( 2x \)[/tex].
- The constant term is [tex]\( 9 \)[/tex].

Putting it all together, the difference of the polynomials is:

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

So, the correct answer is:

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