College

Simplify the expression:

[tex]\left(2x^5 - 7x^3 + x^2 - 4\right) - \left(5x^4 + 4x^2\right)[/tex]

A. [tex]-3x^5 - 7x^3 - 3x^2 - 7[/tex]

B. [tex]7x^5 - 7x^3 + 5x^2 - 1[/tex]

C. [tex]2x^5 + 5x^4 - 7x^3 + 5x^2 - 1[/tex]

D. [tex]2x^5 - 5x^4 - 7x^3 - 3x^2 - 7[/tex]

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 minus sign to the second group:

[tex]$$
2x^5 - 7x^3 + x^2 - 4 - 5x^4 - 4x^2 - 3.
$$[/tex]

Step 2. Rearrange and combine like terms, ordering the terms by descending powers of [tex]$x$[/tex].

- The [tex]$x^5$[/tex] term: [tex]$$2x^5.$$[/tex]
- The [tex]$x^4$[/tex] term: [tex]$$-5x^4.$$[/tex]
- The [tex]$x^3$[/tex] term: [tex]$$-7x^3.$$[/tex]
- The [tex]$x^2$[/tex] terms: [tex]$$x^2 - 4x^2 = -3x^2.$$[/tex]
- The constant terms: [tex]$$-4 - 3 = -7.$$[/tex]

Step 3. Write the simplified polynomial:

[tex]$$
2x^5 - 5x^4 - 7x^3 - 3x^2 - 7.
$$[/tex]

The correct answer corresponds to option D.

Other Questions