Which is the reminder resulted when P is divided by Q? P=(x-2)^2010 + x-2 Q=(x-3)

Expert Answers
hala718 eNotes educator| Certified Educator

P= (x-2)^2010 + x -2

divided by:

Q= (x-3)

Then :

==> P= Q*f + R     Where, f is a function and R is the remainder.

To calculate the remainder , we will substitute with Q's root (3)

P(3) = Q(3) f(3) + R

1+3-2 = R




neela | Student

P(x) = (x-2)^2010+x-2. Q (x) = (x-3).

To find the remainder, R when P(x) is divided by Q(x)/

Let P(x)/Q(x)  = Quotent K(x)  and remaniderR(x).

So, P(x) = Q(x)*K(x) +R, where R a constan R has to be at least one degree less than Q(x) which is x-3.

So (x-2)^2010 +(x-2) = (x-3)K(x) +R. Put x=3 and we get:

(3-2)^2010 +(3-2) = (3-3)K(3) +R.Or

1+1 = 0 +R. Or R = 2.

giorgiana1976 | Student

First, we'll remember the rule of division with reminder.


According to the rule, the degree of the reminder has to be smaller than the degree of Q. In our case, Q is a linear function, so the reminder will be a constant.


First, let's find out the roots of Q.



Now, we'll substitute the root of Q, into the rule of division with reminder:

f(3)=Q(3)*Q1+a, where f(3)=(3-2)^2010 + 3-2 = 1+1=2 and Q(3)=0



The reminder is R=2