High School

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

1. Write Down the Expression for Subtraction:

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

2. Distribute the Negative Sign:

When subtracting, distribute the negative sign to each term in the second polynomial:

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

Notice that subtracting a negative [tex]\(-(-9)\)[/tex] becomes positive (+9).

3. Combine Like Terms:

- Identify and combine like terms (terms with the same power of [tex]\(x\)[/tex]):

For [tex]\(x^3\)[/tex]: There is only one term: [tex]\(5x^3\)[/tex].

For [tex]\(x^2\)[/tex]: Combine [tex]\(4x^2 - 6x^2\)[/tex], which equals [tex]\(-2x^2\)[/tex].

For [tex]\(x\)[/tex]: There's only one term: [tex]\(+2x\)[/tex].

Constant terms: The only constant term is [tex]\(+9\)[/tex].

4. Write the Combined Result:

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

Therefore, the difference between the polynomials is:

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