Question

f(x)=x^3+4x^2-5x+6, I need to find the remainder when f(x) is divided by (x-2). How can I do that?

Answer 1

You could actually do the division (long division).

Or you could use synthetic division: from the divisor (x-2) we'd get divisor 2; from the function f(x), we'd get the coefficients 1, 4, -5 and 6.

This synthetic division problem then becomes:

2 | 1 4 -5 6

_______2__12_14_____
1 6 7 20

and 20 is the remainder. I have little idea of where you're coming from, so why not indicate whether you'd prefer to do this problem using long division or using synthetic division; perhaps then I can guide you through more of either procedure.

Answer 2

Or much easier way...
Plug 2 in the place of in your f expression

Answer 3

we can write f/(x-2) as
f(x)/(x-2)=Q(x)+R/(x-2)
or
f(x)=Q(x)*(x-2)+R
f(2)=Q(2)*(2-2)+R
f(2)=Q(2)*(0)+R
f(2)=0+R
f(2)=R

R represents remainder
Q represents quotient

Answer 4

This is called the remainder theorem

Answer 5

Cool, myininaya!