Answer :
We start with the expression
[tex]$$
\left(2x^5 - 7x^3 + x^2 - 4\right) - \left(5x^4 + 4x^2 + 3\right).
$$[/tex]
Step 1. Distribute the subtraction over the second polynomial:
[tex]$$
2x^5 - 7x^3 + x^2 - 4 - 5x^4 - 4x^2 - 3.
$$[/tex]
Step 2. Rearrange the terms in descending order of powers:
[tex]$$
2x^5 - 5x^4 - 7x^3 + x^2 - 4x^2 - 4 - 3.
$$[/tex]
Step 3. Combine like terms:
- For the [tex]$x^2$[/tex] terms:
[tex]$$
x^2 - 4x^2 = -3x^2.
$$[/tex]
- For the constant terms:
[tex]$$
-4 - 3 = -7.
$$[/tex]
Thus, the expression simplifies to
[tex]$$
2x^5 - 5x^4 - 7x^3 - 3x^2 - 7.
$$[/tex]
This corresponds to option D:
[tex]$$
2x^5 - 5x^4 - 7x^3 - 3x^2 - 7.
$$[/tex]
[tex]$$
\left(2x^5 - 7x^3 + x^2 - 4\right) - \left(5x^4 + 4x^2 + 3\right).
$$[/tex]
Step 1. Distribute the subtraction over the second polynomial:
[tex]$$
2x^5 - 7x^3 + x^2 - 4 - 5x^4 - 4x^2 - 3.
$$[/tex]
Step 2. Rearrange the terms in descending order of powers:
[tex]$$
2x^5 - 5x^4 - 7x^3 + x^2 - 4x^2 - 4 - 3.
$$[/tex]
Step 3. Combine like terms:
- For the [tex]$x^2$[/tex] terms:
[tex]$$
x^2 - 4x^2 = -3x^2.
$$[/tex]
- For the constant terms:
[tex]$$
-4 - 3 = -7.
$$[/tex]
Thus, the expression simplifies to
[tex]$$
2x^5 - 5x^4 - 7x^3 - 3x^2 - 7.
$$[/tex]
This corresponds to option D:
[tex]$$
2x^5 - 5x^4 - 7x^3 - 3x^2 - 7.
$$[/tex]
