## sta880 one year ago 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?

1. mathmale

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.

2. myininaya

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

3. myininaya

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

4. myininaya

This is called the remainder theorem

5. mathmale

Cool, myininaya!