Answer: The required value is [tex]7k^3-k^2-3k+16.[/tex]
Step-by-step explanation: We are given to subtract the polynomial [tex]-2k^3+k^2-9[/tex] from [tex]5k^3-3k+7.[/tex]
That is, we need to find the value of S, where
[tex]S=(5k^3-3k+7)-(-2k^3+k^2-9)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
To perform the given subtraction, we need to combine the like terms as follows :
[tex]S\\\\=(5k^3-3k+7)-(-2k^3+k^2-9)\\\\=5k^3-3k+7+2k^3-k^2+9\\\\=(5+2)k^3-k^2-3k+(9+7)\\\\=7k^3-k^2-3k+16.[/tex]
Thus, the required value is [tex]7k^3-k^2-3k+16.[/tex]
