Answer:
[tex]f(-6)=14[/tex]
Step-by-step explanation:
According to the remainder theorem, if a function f(x) is divided by (x-a), then the remainder is defined by f(a).
It is given that [tex]\dfrac{f(x)}{x+6}[/tex] has a remainder of 14.
Here, the function f(x) is divided by (x+6). So, on comparing (x+6) and (x-a), we get
[tex]a=-6[/tex]
So, by remainder theorem, remainder of [tex]\dfrac{f(x)}{x+6}[/tex] is f(-6).
Since the remainder is 14, therefore
[tex]f(-6)=14[/tex]
Therefore, the answer for first blank is -6 and for second blank is 14, i.e., [tex]f(-6)=14[/tex].
