Answer :
Sure, let's carefully add the polynomials step-by-step:
We are given two polynomials:
[tex]\[ \left(7x^6 + 10x^2 - 10\right) \][/tex]
[tex]\[ \left(3x^6 - 6x^3 + 4\right) \][/tex]
### Steps:
1. Identify like terms: Look at each polynomial and identify the terms with the same degree (exponent).
2. Add the coefficients of like terms:
- For [tex]\( x^6 \)[/tex]: The terms are [tex]\( 7x^6 \)[/tex] and [tex]\( 3x^6 \)[/tex].
[tex]\[ 7x^6 + 3x^6 = 10x^6 \][/tex]
- For [tex]\( x^3 \)[/tex]: Only one term [tex]\( -6x^3 \)[/tex] is present.
[tex]\[ -6x^3 \][/tex]
- For [tex]\( x^2 \)[/tex]: Only one term [tex]\( 10x^2 \)[/tex] is present.
[tex]\[ 10x^2 \][/tex]
- For the constant term (no [tex]\( x \)[/tex]): The terms are [tex]\( -10 \)[/tex] and [tex]\( 4 \)[/tex].
[tex]\[ -10 + 4 = -6 \][/tex]
3. Write the resulting polynomial:
- Combine the results of the additions:
[tex]\[ 10x^6 + 10x^2 - 6x^3 - 6 \][/tex]
### Final Answer:
Combining all the terms, the final polynomial after addition is:
[tex]\[ \boxed{10x^6 - 6x^3 + 10x^2 - 6} \][/tex]
This matches the listed option:
[tex]\[ 10 x^6 - 6 x^3 + 10 x^2 - 6 \][/tex]
We are given two polynomials:
[tex]\[ \left(7x^6 + 10x^2 - 10\right) \][/tex]
[tex]\[ \left(3x^6 - 6x^3 + 4\right) \][/tex]
### Steps:
1. Identify like terms: Look at each polynomial and identify the terms with the same degree (exponent).
2. Add the coefficients of like terms:
- For [tex]\( x^6 \)[/tex]: The terms are [tex]\( 7x^6 \)[/tex] and [tex]\( 3x^6 \)[/tex].
[tex]\[ 7x^6 + 3x^6 = 10x^6 \][/tex]
- For [tex]\( x^3 \)[/tex]: Only one term [tex]\( -6x^3 \)[/tex] is present.
[tex]\[ -6x^3 \][/tex]
- For [tex]\( x^2 \)[/tex]: Only one term [tex]\( 10x^2 \)[/tex] is present.
[tex]\[ 10x^2 \][/tex]
- For the constant term (no [tex]\( x \)[/tex]): The terms are [tex]\( -10 \)[/tex] and [tex]\( 4 \)[/tex].
[tex]\[ -10 + 4 = -6 \][/tex]
3. Write the resulting polynomial:
- Combine the results of the additions:
[tex]\[ 10x^6 + 10x^2 - 6x^3 - 6 \][/tex]
### Final Answer:
Combining all the terms, the final polynomial after addition is:
[tex]\[ \boxed{10x^6 - 6x^3 + 10x^2 - 6} \][/tex]
This matches the listed option:
[tex]\[ 10 x^6 - 6 x^3 + 10 x^2 - 6 \][/tex]
