� Remainder theorem : f( a ) is the remainder when f( x ) is divided by ( x� a)
� q �
f � � is the remainder when f( x ) is divided by ( px � q) � p �
� Partial fractions : 1 . ax � b ( cx �d)( ex � f ) ax � b
2 .
2
( cx � d) can be expressed as
P Q � cx �d ex � f
P Q can be expressed as �
2 cx �d ( cx �d)
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Systems of Equations
�ax �by �c
� � �dx �ey � f
: 2� 2 system
�ax � by � cz � d �
� �ex � fy � gz � h � �ix � jy � kz � l
: 3� 3 system
� The above systems can be solved by PlySmlt2 in TI-84 Plus CE
� Row operations of a system with row R i
:
1 . Multiply the constant k to the row R i
( kR i
)
2 . Add the row R i to the row
R ( Ri � R )
3 . Add the multiple of the row R i to the row j j kR R j
( i
Rj
� )
� Number of solutions of a system with the last row az � b after row operation : 1 . The system has a unique solution if a � 0 2 . The system has no solution if a � 0 and b � 0 3 . The system has infinitely number of solutions if a � 0 and b � 0
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