Answer :
Sure, let's solve the problem step-by-step.
We are given two polynomials:
- [tex]\(7x^6 + 10x^2 - 10\)[/tex]
- [tex]\(3x^6 - 6x^3 + 4\)[/tex]
We need to add these polynomials together.
1. Combine like terms:
- For the [tex]\(x^6\)[/tex] terms: [tex]\(7x^6 + 3x^6 = 10x^6\)[/tex]
- For the [tex]\(x^3\)[/tex] terms: There is no [tex]\(x^3\)[/tex] term in the first polynomial, so we have just [tex]\(-6x^3\)[/tex]
- For the [tex]\(x^2\)[/tex] terms: [tex]\(10x^2\)[/tex] (from the first polynomial) and [tex]\(0x^2\)[/tex] (from the second polynomial), so we have [tex]\(10x^2\)[/tex]
- For the constant terms: [tex]\(-10 + 4 = -6\)[/tex]
Now, putting it all together, the sum of the polynomials is:
[tex]\[10x^6 + 10x^2 - 6x^3 - 6\][/tex]
So, the final simplified polynomial is:
[tex]\[10x^6 - 6x^3 + 10x^2 - 6\][/tex]
Thus, the answer is:
[tex]\[10x^6 - 6x^3 + 10x^2 - 6\][/tex]
Therefore, the correct option is:
[tex]\[10 x^6 - 6 x^3 + 10 x^2 - 6\][/tex]
We are given two polynomials:
- [tex]\(7x^6 + 10x^2 - 10\)[/tex]
- [tex]\(3x^6 - 6x^3 + 4\)[/tex]
We need to add these polynomials together.
1. Combine like terms:
- For the [tex]\(x^6\)[/tex] terms: [tex]\(7x^6 + 3x^6 = 10x^6\)[/tex]
- For the [tex]\(x^3\)[/tex] terms: There is no [tex]\(x^3\)[/tex] term in the first polynomial, so we have just [tex]\(-6x^3\)[/tex]
- For the [tex]\(x^2\)[/tex] terms: [tex]\(10x^2\)[/tex] (from the first polynomial) and [tex]\(0x^2\)[/tex] (from the second polynomial), so we have [tex]\(10x^2\)[/tex]
- For the constant terms: [tex]\(-10 + 4 = -6\)[/tex]
Now, putting it all together, the sum of the polynomials is:
[tex]\[10x^6 + 10x^2 - 6x^3 - 6\][/tex]
So, the final simplified polynomial is:
[tex]\[10x^6 - 6x^3 + 10x^2 - 6\][/tex]
Thus, the answer is:
[tex]\[10x^6 - 6x^3 + 10x^2 - 6\][/tex]
Therefore, the correct option is:
[tex]\[10 x^6 - 6 x^3 + 10 x^2 - 6\][/tex]
