Analysis and Approaches for IBDP Maths Ebook 2 | Page 31

6
Example
Paper 1 Section A – Remainder Theorem
2
When the polynomial
3 2
2x ax bx 1
� � � is divided by ( x � 1) , the remainder is 9, and
when divided by ( x � 2) , it is 3. Find the value of a and the value of b , where a , b� .
[5]
Solution
3 2
2(1) a(1) b 1 9
� � � � (M1) for remainder theorem
2� a�b�1�
9
b�6
� a
A1
3 2
2( �2) � a( �2) �b( �2) �1�
3
�16 � 4a� 2b�1 � 3
��16 � 4a� 2(6 � a) �1� 3
(M1) for substitution
�16 � 4a�12 � 2a�1�
3
6a � 30
a � 5
A1
b �6�
5
b � 1
A1
[5]
Exercise 6
1. When the polynomial
3 2
ax x bx
� � � 3 is divided by ( x � 2) , the remainder is � 13 , and
when divided by ( x � 3) , it is 27. Find the value of a and the value of b , where a ,
b� .
[5]
3 2
2. The same remainder is found when 4x
�2kx
� 5 and
divided by x � 2. Find the possible values of k .
3 2 2
3x
k x 15
� � are
[6]
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