how do you find remainder from the details provided above?Quote:

If P(x) has the remainder -5 when divided by x-3 and the remainder 3 when divided by x+2, find the reminder when P(x) is divided by (x-3)(x+2)

Printable View

- Jan 14th 2009, 12:10 AMhungrybartsfinding P(x) and the remainderQuote:

If P(x) has the remainder -5 when divided by x-3 and the remainder 3 when divided by x+2, find the reminder when P(x) is divided by (x-3)(x+2)

- Jan 14th 2009, 12:27 AMMoo
Imagine you write the euclidean division :

There exists a polynomial Q such that :

Now let

This gives

Same thing for the division by (x+2) : we get

Now what if we consider the division by ?

There exists polynomials R and S (S is the remainder) such that :

Now once again, if you let , you get :

so we have

Similarly, if you let , you get :

So the remainder of P when divided by (x-2)(x+3) will be a polynomial S such that and

But the degree of S cannot exceed 2, since (x-2)(x+3) has a degree 2. (if S has a degree equal or superior to 2, then it still can be divided by (x-2)(x+3))

Hence we're looking for a and b in :

Now the previous working gives you the following system :

Which is very basic algebra :) - Jan 14th 2009, 12:30 AMhungrybarts
how if P(x) was a cubic equation? is it still possible to find P(x)

- Jan 14th 2009, 12:32 AMMoo
- Jan 14th 2009, 02:02 AMmr fantastic
Thread of related interest: http://www.mathhelpforum.com/math-he...mial-help.html

By the way, the question is asking for the remainder so I don't know why you keep talking about P(x). P(x) is**not**the remainder.