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.
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.
