Given that , where is a polynomial.
State the degree of and find the value of and of .
(I am able to deduce the degree i.e. 3
I am also able to find the value of a ,i.e -2 and the value of b, i.e. 1.)
However, the following question linked to the above is what I am not able to solve:
Find also the remainder when is divided by .
(The answer given is -5.)
Hint: Given a polynomial P(x), when you divide it by x - r, the remainder is equal to P(r).
Originally Posted by Ilsa
How do we get the answer -5 then?
If the remainder is Q(-2), how do I further calculate the remainder?
Let's proceed step by step.
(i) Since is of degree 3, assume .
(ii) Put this in RHS. Then by comparing the coefficients of RHS to the coefficients of LHS find the values of and .
(iii) After getting the values of you know the exact expression of . So you can easily put in place of and calculate .
That, actually finding Q, seems to me a very difficult way to do it. Topsquark's suggestion is best. You are told that
and you say you have determined that a= -2 and b= 1 so you have .
Setting x= -2,
so it is easy to find Q(-2) which is, as Topsquark said, the remainder when Q(x) is divided by x+ 2.