Answer :
To add the two polynomials
[tex]$$
\left(2x^4 + 9x^3 + 8x\right) + \left(9x^4 - 7x^3 + 8\right),
$$[/tex]
we follow these steps:
1. Identify like terms:
- The degree 4 terms are [tex]$2x^4$[/tex] and [tex]$9x^4$[/tex].
- The degree 3 terms are [tex]$9x^3$[/tex] and [tex]$-7x^3$[/tex].
- The degree 1 term is [tex]$8x$[/tex].
- The constant term is [tex]$8$[/tex].
2. Combine the like terms for each degree:
- For the [tex]$x^4$[/tex] terms:
[tex]$$
2x^4 + 9x^4 = 11x^4.
$$[/tex]
- For the [tex]$x^3$[/tex] terms:
[tex]$$
9x^3 - 7x^3 = 2x^3.
$$[/tex]
- The [tex]$x$[/tex] term remains as:
[tex]$$
8x.
$$[/tex]
- The constant remains as:
[tex]$$
8.
$$[/tex]
3. Write the final simplified polynomial by combining all the results:
[tex]$$
11x^4 + 2x^3 + 8x + 8.
$$[/tex]
Thus, the sum of the polynomials is
[tex]$$
\boxed{11x^4 + 2x^3 + 8x + 8}.
$$[/tex]
[tex]$$
\left(2x^4 + 9x^3 + 8x\right) + \left(9x^4 - 7x^3 + 8\right),
$$[/tex]
we follow these steps:
1. Identify like terms:
- The degree 4 terms are [tex]$2x^4$[/tex] and [tex]$9x^4$[/tex].
- The degree 3 terms are [tex]$9x^3$[/tex] and [tex]$-7x^3$[/tex].
- The degree 1 term is [tex]$8x$[/tex].
- The constant term is [tex]$8$[/tex].
2. Combine the like terms for each degree:
- For the [tex]$x^4$[/tex] terms:
[tex]$$
2x^4 + 9x^4 = 11x^4.
$$[/tex]
- For the [tex]$x^3$[/tex] terms:
[tex]$$
9x^3 - 7x^3 = 2x^3.
$$[/tex]
- The [tex]$x$[/tex] term remains as:
[tex]$$
8x.
$$[/tex]
- The constant remains as:
[tex]$$
8.
$$[/tex]
3. Write the final simplified polynomial by combining all the results:
[tex]$$
11x^4 + 2x^3 + 8x + 8.
$$[/tex]
Thus, the sum of the polynomials is
[tex]$$
\boxed{11x^4 + 2x^3 + 8x + 8}.
$$[/tex]
