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8. The polynomial   2P x  x  3ax  ax b has x  1 as a factor and leaves a remainder of
–54 when divided by x  2 . Find the values of a and b.

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9. Express as partial fractions.
x 1   x 2  1

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P
P
10. The function P is defined as   x  px  2x  qx 2 where ,p q  .   x is divisible by
x  2 and 8 is the remainder when   x is divided by x  1 .
P
P
(a) Find the value of p and q. Hence, factorize   x completely.
2x  2 6x  1
(b) Express in partial fraction.
P   x

4
3
P
7
P
11. Given the polynomial   x  x  ax  bx  4x  . When   x is divided byx  1 x   1
, the remainder is 2x  5. Find the values of aand b.

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2
P
12. The polynomial   x  x  x  10x a is divisible byx   1 .
(a) By using the Factor Theorem, determine the value of a.
P
(b) Factorize   x completely.

4x  1
(c) Express in partial fractions.
P   x

5x  2 17x  17
13. Express as a sum of partial fractions.
x  2 x   1 2

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14. Given x   3 is one factor of   9 12P x   x  11x  2x . Factorise completely
13x  18
P   x , and express as a sum of partial fractions.
P   x