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58 | P a g e

3
2
1)
30. Given (x  and (x  2) are factors of the polynomial ( ) 2S x  x  px  qx  2 . Find the
values of constants p and q.

4
2
3
31. Given ( )f x  x  5x  8x  .
(a) Show that (x  is a factor of ( )f x .
1)

)
(b) Find the value of a such that ( ) (f x  x  1)(x a .
2
2x  1
2
(c) Hence, express as partial fractions.
f ( )
x

4x  2 9x  17
32. Express ( )S x  in partial fractions
(x  2)(x  2 1)

2
3
33. Given a polynomial ( )P x  mx  nx  1with (2x  1) is one of the factors and ( )P x has a
remainder of 4 when divided by (x-1). Determine the values of m and n. Hence, factorize

completely.

34. A polynomial ( ) 2P x  x  mx  nx  8 gives a remainder of 6x   4 when divided by
3
2
x  1 x   2 . Find the values of m and n.

2
2
3
x
35. Given ( )f x  x  3x   1 and ( )q x  x  3x  5.

1)
(a) Show that (x  is a factor of ( )f x .
(b) Find the values of a, b and c such that ( ) (f x  x  1)(ax  bx  ) c by using long
2
division.

q ( )
x
(c) Hence, express as partial fractions.
f ( )
x

2
3
36. The polynomial   x  mx  nx  2x  gives a remainder 14 when divided by x  and
3
P
 1
a remainder 7 when divided by x   2 . Determine the values of the constants m and n.

2
3
P   7x  x  2 5 Q   x  x  2x   2
x
37. Given and .
(a) Show that x   2 is a factor of   x .
Q