Factor Therom , Remainder Therom

Let f(x) = (bx + c) Q (x) + R where Q (x) is the quotient and R is the remainder which is a constant.

f(-c/b) = { (b)(-c/b)+c } Q(-c/b) + R

= 0+R

= R

Therefore when f(x) is divided by bx+c , the remainder is R where R can be any constants including 0. Both the remainder theorem and the factor theorem are proved.

Hope it helps!

The above is not the proof but only the use of these two theorems.
However, it is not easy to write the proof here.
I guess you just learnt about them and you are not able to understand the proof.

2007-01-11 19:38:45 補充：
The proof should explain why we use f(-c/b) for the theorem.