High School

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 go through the process of adding the two polynomials step-by-step.

We have to add the polynomials:
[tex]\[ (7x^6 + 10x^2 - 10) \][/tex]
and
[tex]\[ (3x^6 - 6x^3 + 4). \][/tex]

First, let's align the similar terms from both polynomials.

### Like terms in the two polynomials:
- [tex]\( x^6 \)[/tex] terms: [tex]\( 7x^6 \)[/tex] and [tex]\( 3x^6 \)[/tex]
- [tex]\( x^3 \)[/tex] terms: there is no [tex]\( x^3 \)[/tex] term in the first polynomial and [tex]\( -6x^3 \)[/tex] in the second
- [tex]\( x^2 \)[/tex] terms: [tex]\( 10x^2 \)[/tex] in the first polynomial and no [tex]\( x^2 \)[/tex] term in the second
- Constant terms: [tex]\( -10 \)[/tex] from the first polynomial and [tex]\( 4 \)[/tex] from the second

Next, add the coefficients of the like terms:

1. Term [tex]\( x^6 \)[/tex]:
[tex]\[
7x^6 + 3x^6 = 10x^6
\][/tex]

2. Term [tex]\( x^3 \)[/tex]:
[tex]\[
0x^3 - 6x^3 = -6x^3
\][/tex]

3. Term [tex]\( x^2 \)[/tex]:
[tex]\[
10x^2 + 0x^2 = 10x^2
\][/tex]

4. Constant term:
[tex]\[
-10 + 4 = -6
\][/tex]

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

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

This matches with:
[tex]\[
10 x^6-6 x^3+10 x^2-6
\][/tex]

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