Question

What does the remainder theorem conclude given that f(x)/x+6 has a remainder of 14? Enter your answer by filling in the boxes.​

Answer 1

`f(-6)=14`

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
`(f(x))/(x+6)` 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

`a=-6`

So, by remainder theorem, remainder of
`(f(x))/(x+6)` is f(-6).

Since the remainder is 14, therefore

`f(-6)=14`

Therefore, the answer for first blank is -6 and for second blank is 14, i.e.,
`f(-6)=14`.