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59 | P a g e

Q
(b) Factorize   x completely.
P   x
(c) Express as partial fractions.
Q   x

38. (a) When a polynomial   x is divided by x   2 andx   3 the remainders
P
P
R
are 5 and l0 respectively. Find the remainder   x , when   x is divided
by x  2 x   3 where   x  ax b , a and b are constants.

R


44 10x
(b) State the factors of 2x  2 5x  3. Hence, express as partial
(x  3)(2x  5x  3)
2
fractions.

   ax b
P x
39. Given a polynomial of degree 3,   x  2 x  3 Q x   where a and b are
constant.

(a) ( ) has the remainder −18 and 17 when divided by ( + 2) and ( − 3)
respectively. Find the values of a and b, and state the remainder when ( ) is divided
by ( + 2)( − 3)


(b) Let ( )Q x  mx n. Use the values of a and b in part 39(a) to determine ( ) if the
coefficient of x in ( ) is 2 and   4P  42.
3

x  12
(c) Express in partial fraction.
x  2  x  2  3