The remainder theorem is an easy way of calculating the remainder from polynomial division.
The conclusion of remainder theorem, here is that: [tex]f(-5) = 17[/tex]
We have:
[tex]\frac{f(x)}{x + 5}[/tex] and a remainder of 17
The general rule of the remainder theorem is that:
For [tex]\frac{f(x)}{x + a}[/tex] and a remainder of b
It means:
[tex]f(-a) = b[/tex]
By comparing
[tex]\frac{f(x)}{x + a}[/tex] and [tex]\frac{f(x)}{x + 5}[/tex]
It means:
[tex]a = 5[/tex] and [tex]b = 17[/tex]
So:
[tex]f(-a) = b[/tex] becomes
[tex]f(-5) = 17[/tex]
Hence, the conclusion is that:
[tex]f(-5) = 17[/tex]
Read more about remainder theorems at:
https://brainly.com/question/13416073
