Answer: The required sum is [tex]6x^4-x^3-5x^2+10x+5.[/tex]
Step-by-step explanation: We are given to find the following sum:
[tex]S=(2x^4+x^3-4x^2+3)+(4x^4-2x^3-x^2+10x+2).[/tex]
To find the sum, we need to add the coefficients of the same exponents of the unknown variable x.
The summation is as follows:
[tex]S\\\\=(2x^4+x^3-4x^2+3)+(4x^4-2x^3-x^2+10x+2)\\\\=(2+4)x^4+(1-2)x^3+(-4-1)x^2+10x+(3+2)\\\\=6x^4+(-1)x^3+(-5)x^2+10x+5\\\\=6x^4-x^3-5x^2+10x+5.[/tex]
Thus, the required sum is [tex]6x^4-x^3-5x^2+10x+5.[/tex]
