The sum of given expression is [tex]10x^{4} -x^{3} -7x^{2} -2x+12[/tex].
Given expression is,
[tex](2x^4 + 5x^3 - 8x^2 - x+10)[/tex] and [tex](8x^4 - 4x^3 + x^2 - x + 2)[/tex].
We have to find the sum of both expression.
Since both the term contains same variable x, so
[tex]2x^4 + 5x^3 - 8x^2 - x+10+8x^4 - 4x^3 + x^2 - x + 2[/tex]
on arranging the terms we get,
[tex]2x^4+8x^4+5x^3-4x^3-8x^2+x^2-x-x+10+2[/tex]
adding like terms, we get
[tex]10x^{4} -x^{3} -7x^{2} -2x+12[/tex] .
Hence the required expression is [tex]10x^{4} -x^{3} -7x^{2} -2x+12[/tex].
For more details on polynomial addition follow the link:
https://brainly.com/question/4420925
