Answer :
We start with the expression
[tex]$$
\left(4 x^3 - 2 x^2 + 5\right) - \left(3 x^3 + x - 4\right).
$$[/tex]
Step 1: Remove Parentheses
When subtracting, it is important to distribute the negative sign to each term in the second polynomial. This gives:
[tex]$$
4x^3 - 2x^2 + 5 - 3x^3 - x + 4.
$$[/tex]
Step 2: Combine Like Terms
Group the terms with the same power of [tex]$x$[/tex]:
- Combine the [tex]$x^3$[/tex] terms:
[tex]$$
4x^3 - 3x^3 = x^3.
$$[/tex]
- The [tex]$x^2$[/tex] term remains as is:
[tex]$$
-2x^2.
$$[/tex]
- Combine the [tex]$x$[/tex] terms:
[tex]$$
-x.
$$[/tex]
- Combine the constant terms:
[tex]$$
5 + 4 = 9.
$$[/tex]
Step 3: Write the Result
Putting the combined terms together, the resulting polynomial is:
[tex]$$
x^3 - 2x^2 - x + 9.
$$[/tex]
Comparing this with the given options, we see that it matches option B:
[tex]$$
x^3 - 2x^2 - x + 9.
$$[/tex]
Thus, the final answer is option B.
[tex]$$
\left(4 x^3 - 2 x^2 + 5\right) - \left(3 x^3 + x - 4\right).
$$[/tex]
Step 1: Remove Parentheses
When subtracting, it is important to distribute the negative sign to each term in the second polynomial. This gives:
[tex]$$
4x^3 - 2x^2 + 5 - 3x^3 - x + 4.
$$[/tex]
Step 2: Combine Like Terms
Group the terms with the same power of [tex]$x$[/tex]:
- Combine the [tex]$x^3$[/tex] terms:
[tex]$$
4x^3 - 3x^3 = x^3.
$$[/tex]
- The [tex]$x^2$[/tex] term remains as is:
[tex]$$
-2x^2.
$$[/tex]
- Combine the [tex]$x$[/tex] terms:
[tex]$$
-x.
$$[/tex]
- Combine the constant terms:
[tex]$$
5 + 4 = 9.
$$[/tex]
Step 3: Write the Result
Putting the combined terms together, the resulting polynomial is:
[tex]$$
x^3 - 2x^2 - x + 9.
$$[/tex]
Comparing this with the given options, we see that it matches option B:
[tex]$$
x^3 - 2x^2 - x + 9.
$$[/tex]
Thus, the final answer is option B.
