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

1. Write down the polynomials you are subtracting:
- First polynomial: [tex]\(5x^3 + 4x^2\)[/tex]
- Second polynomial: [tex]\(6x^2 - 2x - 9\)[/tex]

2. Subtract the second polynomial from the first polynomial:
[tex]\[
(5x^3 + 4x^2) - (6x^2 - 2x - 9)
\][/tex]

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

4. 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]

5. Write the resulting polynomial:
[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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