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

*print*Print*list*Cite

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.

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

P=Q*Q1+R

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.

R=a

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

x-3=0

x=3

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

2=0+a

**a=2**

**The reminder is R=2**