College

Add [tex]\left(7x^6 + 10x^2 - 10\right) + \left(3x^6 - 6x^3 + 4\right)[/tex]

A. [tex]10x^6 + 4x^2 - 6[/tex]

B. [tex]10x^6 + 4x^3 - 6[/tex]

C. [tex]10x^6 - 6x^3 + 10x^2 - 6[/tex]

D. [tex]10x^6 + 10x^2 - 6x^3 + 6[/tex]

Answer :

Sure, let's solve the problem step-by-step.

We are given two polynomials:
[tex]\[
P(x) = 7x^6 + 10x^2 - 10
\][/tex]
[tex]\[
Q(x) = 3x^6 - 6x^3 + 4
\][/tex]

We need to add these two polynomials together:
[tex]\[
P(x) + Q(x) = (7x^6 + 10x^2 - 10) + (3x^6 - 6x^3 + 4)
\][/tex]

Let's combine like terms by aligning the polynomials accordingly:
[tex]\[
(7x^6 + 3x^6) + (-6x^3) + (10x^2) + (-10 + 4)
\][/tex]

Now, perform the addition for like terms:
1. Combine the [tex]\(x^6\)[/tex] terms:
[tex]\[
7x^6 + 3x^6 = 10x^6
\][/tex]

2. The [tex]\(x^3\)[/tex] term remains as is:
[tex]\[
-6x^3
\][/tex]

3. The [tex]\(x^2\)[/tex] term remains as is:
[tex]\[
10x^2
\][/tex]

4. Combine the constant terms:
[tex]\[
-10 + 4 = -6
\][/tex]

Putting it all together, we get:
[tex]\[
10x^6 - 6x^3 + 10x^2 - 6
\][/tex]

Thus, the final result is:
[tex]\[
10x^6 - 6x^3 + 10x^2 - 6
\][/tex]

So, the correct answer is:
[tex]\[
10x^6 - 6x^3 + 10x^2 - 6
\][/tex]

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