Answer :
Sure! Let's add these two polynomials step-by-step:
1. Write down the given polynomials:
[tex]\[
\text{First polynomial: } 8x^8 - 9x^3 + 3x^2 + 9
\][/tex]
[tex]\[
\text{Second polynomial: } 4x^7 + 6x^3 - 2x
\][/tex]
2. Align and add the polynomials:
When adding polynomials, you add the coefficients of like terms. That means we need to combine terms that have the same powers of [tex]\(x\)[/tex].
- For [tex]\(x^8\)[/tex]: There is only one term, [tex]\(8x^8\)[/tex], from the first polynomial.
- For [tex]\(x^7\)[/tex]: There is only one term, [tex]\(4x^7\)[/tex], from the second polynomial.
- For [tex]\(x^3\)[/tex]: Combine [tex]\(-9x^3\)[/tex] from the first polynomial and [tex]\(6x^3\)[/tex] from the second polynomial. Add them: [tex]\(-9 + 6 = -3\)[/tex].
- For [tex]\(x^2\)[/tex]: There is only one term, [tex]\(3x^2\)[/tex], from the first polynomial.
- For [tex]\(x\)[/tex]: There is only one term, [tex]\(-2x\)[/tex], from the second polynomial.
- Constant term (no [tex]\(x\)[/tex]): There is only one term, [tex]\(9\)[/tex], from the first polynomial.
3. Write the combined polynomial:
[tex]\[
8x^8 + 4x^7 - 3x^3 + 3x^2 - 2x + 9
\][/tex]
So, the final answer is:
D. [tex]\(8x^8 + 4x^7 - 3x^3 + 3x^2 - 2x + 9\)[/tex]
1. Write down the given polynomials:
[tex]\[
\text{First polynomial: } 8x^8 - 9x^3 + 3x^2 + 9
\][/tex]
[tex]\[
\text{Second polynomial: } 4x^7 + 6x^3 - 2x
\][/tex]
2. Align and add the polynomials:
When adding polynomials, you add the coefficients of like terms. That means we need to combine terms that have the same powers of [tex]\(x\)[/tex].
- For [tex]\(x^8\)[/tex]: There is only one term, [tex]\(8x^8\)[/tex], from the first polynomial.
- For [tex]\(x^7\)[/tex]: There is only one term, [tex]\(4x^7\)[/tex], from the second polynomial.
- For [tex]\(x^3\)[/tex]: Combine [tex]\(-9x^3\)[/tex] from the first polynomial and [tex]\(6x^3\)[/tex] from the second polynomial. Add them: [tex]\(-9 + 6 = -3\)[/tex].
- For [tex]\(x^2\)[/tex]: There is only one term, [tex]\(3x^2\)[/tex], from the first polynomial.
- For [tex]\(x\)[/tex]: There is only one term, [tex]\(-2x\)[/tex], from the second polynomial.
- Constant term (no [tex]\(x\)[/tex]): There is only one term, [tex]\(9\)[/tex], from the first polynomial.
3. Write the combined polynomial:
[tex]\[
8x^8 + 4x^7 - 3x^3 + 3x^2 - 2x + 9
\][/tex]
So, the final answer is:
D. [tex]\(8x^8 + 4x^7 - 3x^3 + 3x^2 - 2x + 9\)[/tex]
