DATE
I 2 tues
the remainder theorem
- If a polynomial p(x) is divided by X-C, then the remainder
is equal to p(c)
e.g. Determine the remainder when the given polynomial P (x)
is divided by the given divisor X - C
a. P (x) = 2x , - 7 X 2 - 5x + 4 i X - 4
p(4) : 2 ( 4) - 7(4)2 & - 5(4) + 4
p (4) = 2 (64) - 7(16) - 20 + 4
p (4) = 0, o
no
remainder!
D. p (x) = 2 x 3 - 7x 2 + 3x + 4 ; x-1
p (+1) = 2 (+1) 3. 7(+1) & + 3 (+1) + 4
P (+1) = 2-7 + 3 + 4
R = p (1) =2 =
C. P (X) : X 87 + 2x 48 + 7; X + I
p (-1) = (-1) 87 + 2(-1) + 7
p (-1) = I + 2 + 7 = 8H 8 = R
d.p (x) = 2x 7 - 3x 5 + 4 x s - 5x + 3; X - 2
P (2) : 2(2)7 - 3(2) 5 . 4(2) - 5(2) + 3
p(2) : 189 = R
H
e. p(x) = 5 X 3 + 4 X 2 - 31 X + 6 ; 5 x - I
5x- 1=0
X = 1
P ('15) = 5 ('15) 5 + 4 ('1s)2 2 - 31 (15) + 6
5
R = of 0 #
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