Summary MAT1511 ASSIGNMENT 2 2024

MAT1511
ASSIGNMENT 2
2024

, QUESTION 1




Solution:



a).



By long division :



( x + 12 )=0
−1
x=
2


−1
2 1531 20 4
2
−1−7−12−4
2 14 24 8 0



Sincethe remainder is zero , then x +( 12 ) is a factor of P ( x ) .
b).



P ( x )=2 x 4 + 15 x 3 +31 x2 +20 x +4



( 12 ) (2 x +14 x +24 x +8)
P ( x )= x + 3 2




p=4∧q=2

, factors of p
Possibe zeros=
factors of q
± { 1,2,4 }
Possibe zeros=
± { 1,2 }
1
Possibe zeros=± 1 ,± , ±2 , ± 4
2




c).



Try x=1:
1 215 31 20 4
2 17 48 68
2 17 48 68 72


Sincethe remainder is not 0 ,then x =1is not a root


Try x=−1 :
−1 215 31 20 4
−2−13−18−2
2 1318 2 2


Sincethe remainder is not 0 ,then x =−1is not aroot


1
Try x= :
2
1
215 31 20 4
2
39 39
18
2 4
39 55
2 16 39
2 4