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4x 3
21. Express in partial fractions.
2
x 2  x  2x  2

2
3
22. Given a polynomial   2P x  x  ax  bx 30 has factors x  2 and x  5 .
(a) Find the value of the constants a and b.

P
(b) Factorize   x completely.

5x  2 14x  13 A B C
23. By writing in the form of the partial fractions   , find A,
2
x  3x   3 x  3 x  1 x  1
3
x
B and C .

2
3
24. When   3P x  x  px  qx  3 is divided by x  2 x  2 , the remainder is 8x  .
1
By using the Remainder Theorem, find the values of p and q. Hence, obtain the quotient.

2
3
6
x
25. Given   2f x  x  5x   .
f
(a) Show thatx   2 is a factor of   x .
2
f x
(b) Find a, b and c such that   x  2 ax  bx   c .
x  4
(c) Express as partial fractions.
f   x

3
2
2
26. Given that ax b is a remainder when polynomial 2x  5x  28x  15 is divided by x  1
. By using the remainder theorem, find the value of a and b .

4
27. Express in the form of partial fractions.
x  1  x  2  9

2
3
28. The polynomial ( ) 5S x  x  px  qx  1 gives a remainder of 26 on division by (x  1) and
remainder of –8 on division by (x  . Find the values of the constants p and q.
1)

29. Given ( ) 10P x  x  6x  11 and ( )  x  5x  8x 
3
2
2
x
Q
4
x
(a) Show that (x  1) is a factor of ( ) .
Q
(b) Factorise ( )Q x completely.
P ( )
x
(c) Express as partial fractions.
Q ( )
x