High School

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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 :

We want to find the difference between the two polynomials:

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

Step 1: Remove the Parentheses

When subtracting the second polynomial, distribute the negative sign to each of its terms:

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

Step 2: Combine Like Terms

- The term [tex]$5x^3$[/tex] stands alone.
- For the [tex]$x^2$[/tex] terms: [tex]$4x^2 - 6x^2 = -2x^2$[/tex].
- The term [tex]$2x$[/tex] remains as is.
- The constant term is [tex]$9$[/tex].

Thus, the simplified expression becomes:

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

This is the final result for the difference of the polynomials.

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