Given:
The function is
[tex]f(x)=2x^4-4x^3+20x-100[/tex]
To find:
The remainder if f(x) is divided by (x+11).
Solution:
According to the remainder theorem, if a function f(x) is divided by (x-c), then the remainder is f(c).
On comparing (x+11) and (x-c), we get c=-11.
Using remainder theorem, if a function f(x) is divided by (x+11), then the remainder is f(-11).
Putting x=-11 in the given function.
[tex]f(-11)=2(-11)^4-4(-11)^3+20(-11)-100[/tex]
[tex]f(-11)=29282+5324-220-100[/tex]
[tex]f(-11)=34606-320[/tex]
[tex]f(-11)=34286[/tex]
Therefore, the remainder is 34286 when f(x) is divided by (x+11).
