Answer :
To find the difference of the polynomials
[tex]$$\left(5x^3 + 4x^2\right) - \left(6x^2 - 2x - 9\right),$$[/tex]
we follow these steps:
1. Distribute the minus sign:
When subtracting the second polynomial, distribute the minus sign to every term inside the parentheses:
[tex]$$
(5x^3 + 4x^2) - 6x^2 + 2x + 9.
$$[/tex]
2. Combine like terms:
- The only cubic term is [tex]$5x^3$[/tex].
- Combine the quadratic terms: [tex]$4x^2 - 6x^2 = -2x^2$[/tex].
- The linear term is [tex]$2x$[/tex].
- The constant is [tex]$9$[/tex].
This gives:
[tex]$$
5x^3 - 2x^2 + 2x + 9.
$$[/tex]
3. Write the final answer:
The difference of the polynomials is
[tex]$$
\boxed{5x^3 - 2x^2 + 2x + 9}.
$$[/tex]
This is the simplified form of the difference between the two given polynomials.
[tex]$$\left(5x^3 + 4x^2\right) - \left(6x^2 - 2x - 9\right),$$[/tex]
we follow these steps:
1. Distribute the minus sign:
When subtracting the second polynomial, distribute the minus sign to every term inside the parentheses:
[tex]$$
(5x^3 + 4x^2) - 6x^2 + 2x + 9.
$$[/tex]
2. Combine like terms:
- The only cubic term is [tex]$5x^3$[/tex].
- Combine the quadratic terms: [tex]$4x^2 - 6x^2 = -2x^2$[/tex].
- The linear term is [tex]$2x$[/tex].
- The constant is [tex]$9$[/tex].
This gives:
[tex]$$
5x^3 - 2x^2 + 2x + 9.
$$[/tex]
3. Write the final answer:
The difference of the polynomials is
[tex]$$
\boxed{5x^3 - 2x^2 + 2x + 9}.
$$[/tex]
This is the simplified form of the difference between the two given polynomials.
