Answer :
Sure! Let's add the two polynomials together step-by-step.
We have the two polynomials:
1. [tex]\( 7x^6 + 10x^2 - 10 \)[/tex]
2. [tex]\( 3x^6 - 6x^3 + 4 \)[/tex]
To add these polynomials, we should combine the like terms, which are terms having the same power of [tex]\( x \)[/tex].
1. Combine the [tex]\( x^6 \)[/tex] terms:
- The coefficient from the first polynomial is 7.
- The coefficient from the second polynomial is 3.
- Adding these together gives: [tex]\( 7 + 3 = 10 \)[/tex].
- So, the combined term is [tex]\( 10x^6 \)[/tex].
2. Combine the [tex]\( x^3 \)[/tex] terms:
- The first polynomial doesn't have an [tex]\( x^3 \)[/tex] term, so its coefficient is 0.
- The coefficient from the second polynomial is -6.
- Adding these together gives: [tex]\( 0 - 6 = -6 \)[/tex].
- So, the combined term is [tex]\( -6x^3 \)[/tex].
3. Combine the [tex]\( x^2 \)[/tex] terms:
- The coefficient from the first polynomial is 10.
- The second polynomial doesn't have an [tex]\( x^2 \)[/tex] term, so its coefficient is 0.
- Adding these together gives: [tex]\( 10 + 0 = 10 \)[/tex].
- So, the combined term is [tex]\( 10x^2 \)[/tex].
4. Combine the constant terms:
- The constant from the first polynomial is -10.
- The constant from the second polynomial is 4.
- Adding these gives: [tex]\( -10 + 4 = -6 \)[/tex].
Combining all these results, the sum of the polynomials is:
[tex]\[ 10x^6 - 6x^3 + 10x^2 - 6 \][/tex]
The correct answer from the provided options is:
[tex]\[ 10x^6 - 6x^3 + 10x^2 - 6 \][/tex]
We have the two polynomials:
1. [tex]\( 7x^6 + 10x^2 - 10 \)[/tex]
2. [tex]\( 3x^6 - 6x^3 + 4 \)[/tex]
To add these polynomials, we should combine the like terms, which are terms having the same power of [tex]\( x \)[/tex].
1. Combine the [tex]\( x^6 \)[/tex] terms:
- The coefficient from the first polynomial is 7.
- The coefficient from the second polynomial is 3.
- Adding these together gives: [tex]\( 7 + 3 = 10 \)[/tex].
- So, the combined term is [tex]\( 10x^6 \)[/tex].
2. Combine the [tex]\( x^3 \)[/tex] terms:
- The first polynomial doesn't have an [tex]\( x^3 \)[/tex] term, so its coefficient is 0.
- The coefficient from the second polynomial is -6.
- Adding these together gives: [tex]\( 0 - 6 = -6 \)[/tex].
- So, the combined term is [tex]\( -6x^3 \)[/tex].
3. Combine the [tex]\( x^2 \)[/tex] terms:
- The coefficient from the first polynomial is 10.
- The second polynomial doesn't have an [tex]\( x^2 \)[/tex] term, so its coefficient is 0.
- Adding these together gives: [tex]\( 10 + 0 = 10 \)[/tex].
- So, the combined term is [tex]\( 10x^2 \)[/tex].
4. Combine the constant terms:
- The constant from the first polynomial is -10.
- The constant from the second polynomial is 4.
- Adding these gives: [tex]\( -10 + 4 = -6 \)[/tex].
Combining all these results, the sum of the polynomials is:
[tex]\[ 10x^6 - 6x^3 + 10x^2 - 6 \][/tex]
The correct answer from the provided options is:
[tex]\[ 10x^6 - 6x^3 + 10x^2 - 6 \][/tex]
