Answer :
Sure! Let's solve the given problem step-by-step by performing the addition of the two polynomials [tex]\((7x^3 - 9x^2 - 5)\)[/tex] and [tex]\((2x^3 + 4x^2 - 2x + 6)\)[/tex].
1. Write down the polynomials and align their like terms:
[tex]\[
(7x^3 - 9x^2 - 5) + (2x^3 + 4x^2 - 2x + 6)
\][/tex]
2. Combine the like terms:
- For [tex]\(x^3\)[/tex]: [tex]\(7x^3 + 2x^3 = 9x^3\)[/tex]
- For [tex]\(x^2\)[/tex]: [tex]\(-9x^2 + 4x^2 = -5x^2\)[/tex]
- For [tex]\(x\)[/tex]: There is no [tex]\(x\)[/tex]-term in the first polynomial, so we just have [tex]\(-2x\)[/tex]
- For the constants: [tex]\(-5 + 6 = 1\)[/tex]
3. Write down the resulting polynomial:
[tex]\[
9x^3 - 5x^2 - 2x + 1
\][/tex]
So the final answer in standard form is:
[tex]\[
9x^3 - 5x^2 - 2x + 1
\][/tex]
The correct choice from the options provided is:
```
9x^3 - 5x^2 - 2x + 1
```
1. Write down the polynomials and align their like terms:
[tex]\[
(7x^3 - 9x^2 - 5) + (2x^3 + 4x^2 - 2x + 6)
\][/tex]
2. Combine the like terms:
- For [tex]\(x^3\)[/tex]: [tex]\(7x^3 + 2x^3 = 9x^3\)[/tex]
- For [tex]\(x^2\)[/tex]: [tex]\(-9x^2 + 4x^2 = -5x^2\)[/tex]
- For [tex]\(x\)[/tex]: There is no [tex]\(x\)[/tex]-term in the first polynomial, so we just have [tex]\(-2x\)[/tex]
- For the constants: [tex]\(-5 + 6 = 1\)[/tex]
3. Write down the resulting polynomial:
[tex]\[
9x^3 - 5x^2 - 2x + 1
\][/tex]
So the final answer in standard form is:
[tex]\[
9x^3 - 5x^2 - 2x + 1
\][/tex]
The correct choice from the options provided is:
```
9x^3 - 5x^2 - 2x + 1
```
