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2
3

15. A polynomial has the form   2P x  x  3x  px q , with x real and p, q constants.
When   x is divided by x  the remainder is 2 4x .Find the values of p and q, and
P
 1
P
factorize   x completely if 2 is one of the roots.

2

3
16. Polynomial   2P x  x  ax  x b has x   1 as a factor and leaves a remainder 12 when
divided by x   3 . Determine the values of a and b.

2
3
P
17. Two factors of the polynomial   x  x  ax  bx  6 are x   1 and x   2 . Determine
the values of a and b, and find the third factor of the polynomial.
2x  2 5x  13
Hence, express as a sum of partial fractions.
P   x

3
2
P
6
18. (a) Show that x   3 is a factor of polynomial   x  x  2x  5x .
P
Hence, factorize   x completely.

2

f
 1
(b) If   x  ax  bx c leaves remainder 1, 25 and 1 on division by x  , x   1
and x   2 respectively, find the values of a, b and c. Hence, show that   x has
f
two equal real roots.

2x  1
19. Express in partial fractions.
(x  2)(x  2x  4)
2

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

20. (a) Find a cubic polynomial ( ) (Q x  x a )(x b )(x c satisfying the following
)
conditions:
3
The coefficients of x is 1, Q( 1)  0,Q(2)  and Q(3)   8.
0
3
2
(b) A polynomial ( )P x  ax  4x  bx  18 has a factor x   2 and a remainder 16
when divided byx   1 . Find the values of a and b. Hence, factorise P ( )
x
completely.