Answer :

Sure! Let's solve the given problem step by step.

We need to add the polynomials [tex]\((2x^7 - 5)\)[/tex] and [tex]\(4x^7\)[/tex].

1. Identify Like Terms:
Polynomials are added by combining like terms. Like terms have the same variable raised to the same power.

In this case, [tex]\(2x^7\)[/tex] and [tex]\(4x^7\)[/tex] are like terms because they both have [tex]\(x^7\)[/tex].

2. Combine the Like Terms:
We will add the coefficients of [tex]\(x^7\)[/tex].

- The coefficient of the first term [tex]\(2x^7\)[/tex] is 2.
- The coefficient of the second term [tex]\(4x^7\)[/tex] is 4.

So, we add these coefficients together:
[tex]\[
2 + 4 = 6
\][/tex]

Therefore, when we add these terms, we get:
[tex]\[
(2x^7) + (4x^7) = 6x^7
\][/tex]

3. Combine the Constant Term as Well:
We also have a constant term in the first polynomial [tex]\(-5\)[/tex].

So, the final result after adding the polynomials is:
[tex]\[
6x^7 - 5
\][/tex]

The simplified result is:
[tex]\[
6x^7 - 5
\][/tex]

This is the correct answer.