Question

If x​​​​​​^{​​​​​​5} - 9x² ​+ 12x -14 is divisible by x-3, what is the remainder?

Answer 1

You are wrong..When a number is divisible by another ,the remainder may or may not be 0 .
if Number is divisible by it's divisor ,then only remainder should be zero. else it has some remainder..

here,
f(x)=x​​​​​​^{​​​​​​5} - 9x² ​+ 12x -14 is divisible by (x-3) . then got remainder as 184. then we can conclude by remainder theorem :
(x-3) is not a factor/divisor of f(x)
so , f(3) = 184

Another Example:
------> f(x)=x​​​​​​^{​​​​​​3} - 12x² ​- 42 is divisible by (x-3) . then got remainder as -123. Therefore f(3) = -123

I hope you understand....thank you...