College

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 given polynomials, we will follow these steps:

1. Identify the Polynomials:

The polynomials given are:
- First polynomial: [tex]\(5x^3 + 4x^2\)[/tex]
- Second polynomial: [tex]\(6x^2 - 2x - 9\)[/tex]

2. Subtract the Second Polynomial from the First:

We need to subtract the second polynomial from the first polynomial. This means we will distribute the negative sign across the second polynomial and then combine like terms.

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

3. Distribute the Negative Sign:

Distribute the negative sign across the second polynomial:
[tex]\[
(5x^3 + 4x^2) - 6x^2 + 2x + 9
\][/tex]

4. Combine Like Terms:

Now, combine the terms of the polynomials:

- The terms with [tex]\(x^3\)[/tex] are: [tex]\(5x^3\)[/tex]
- The terms with [tex]\(x^2\)[/tex] are: [tex]\(4x^2 - 6x^2 = -2x^2\)[/tex]
- The terms with [tex]\(x\)[/tex] are: [tex]\(+2x\)[/tex]
- The constant terms are: [tex]\(+9\)[/tex]

5. Write the Final Difference:

The simplified polynomial, after combining like terms, is:
[tex]\[
5x^3 - 2x^2 + 2x + 9
\][/tex]

This is the difference of the given polynomials.

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