Somebody please explain the remainder theorem :(

Question

anonymous · Answer

If a(x) is dividend, b(x) is divisor and q(x) is quotient , there exists one polynomial r(x) which satisfies the equation for all values of x.
Equation :
a(x) = b(x).q(x)+r(x)

anonymous · Answer

i forgot it.. so tried to interpret in my own language :P

anonymous · Answer

ohhh, thats simple. i will explain with a example. so if you have $$x^3 + 2x^2 +5x + 3$$, hypothetically (i made it up) and that is equal to (x-2)Q(x) +R. Q(x) is a quadratic, and R is the remainder. basically, you have to find a value for x, in this case 2, that will eliminate  the Q(x), and then you can equate your equation and solve it. it's all very simple.

anonymous · Answer

a = bq+r is the integer version of the above.

anonymous · Answer

lol i ran here hoping it was CRT

anonymous · Answer

what is CRT?

anonymous · Answer

it is possible that the "remainder theorem" mean in this case that if you divide 
a polynomial P by 
$$x-r$$ then the remainder is 
$$P(r)$$

anonymous · Answer

@tanvida chinese remainder theorem

anonymous · Answer

ohh :P XD

anonymous · Answer

@louise if you want to write the theorem, maybe it would be clearer and you would get a better answer with an example