Find the value of a and b so that x2-4 is a factor of ax4+2x3-3x2+bx-4.
x2-4
x2-22
(x+2)(x-2)
Let p(x)=ax4+2x3-3x2+bx-4
(x+2) and (x-2) are the factors of p(x)
p(-2)=0
a(-2)4+2(-2)3-3(-2)2+b(-2)-4
=0
16a-16-12-2b-4=0
16a-2b-32=0 ..(1)
p(2)=0
a(2)4+2(2)3-3(2)2+b(2)-4
=0
16a+16-12+2b-4=0
16a+2b=0 ..(2)
Equating 1 and 2
16a-2b-32=16a+2b
-4b=32
b=-8
From 2
16a+2b=0
16a-16=0
a=16/16
a=1