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Elly fat mn 3omry ( 1 – 1 )

Multiplication of Polynomials
Examples
(a) a ( b + c + … ) = a b + a c + ...
2
2
(b) 5 x (3 x – 2 x + 6 ) = ( 5 x ) ( 3 x ) + ( 5 x ) ( – 2 x ) + ( 5 x ) ( 6 )
3
2
= 15 x – 10 x + 30 x
2
2
(c) ( x – 3 x + 2 ) ( x – 5 ) = x ( x – 5 ) – 3 x ( x – 5 ) + 2 ( x – 5 )
2
3
2
= x – 5 x – 3 x + 15 x + 2 x – 10
3
2
= x – 8 x + 17 x – 10
Division of Polynomials

Example
3
2
9 x  6 x  12 x = 9 x 3   6 x  12 x = 3x  2 x 
2
4
3x 3x 3x 3x

Example
x  2 x  4
3
x  2

First method: Second method: Synthetic division
x  2 x  2
2
x  2 x 3  2 x  4  2 1  0  2  4

x  2 x 2  2 4  4
3
2
 2 x  2 x  4 1  2 2 0
 2 x  4 x 1x 2  2 x  2
2
2 x  4
2 x  4

0
3
x  2 x  4
2
 = x – 2 x +2
x  2

Synthetic division can also be used with divisors of the type a x + b. We will only use
synthetic division when the divisor is the form x – a .

Remember:

If P ( x ) is a polynomial and P ( a ) = 0 , then ( x – a ) is a factor of P ( x ).

Calculus 4 Unit (1)