Answer:
a= 2, b=1 and c=-8
Explanation:
+ f(x) is exactly dividsible by (2x-3), that means f(x)= (2x-3). g(x), then f(3/2)= 0
+ f(x) is divided by (x-2) and the remainder is 12, that means f(x)=(x-2). h(x) +12
So f(2)=12.
+ The last: f(x)=(x+3). k(x)+72, so f(-3)=72
Then we have 3 equations:
f(3/2)=0
f(2)=12
f(-3)=72
So we replace and we find:
81a+54b+36c=-72
16a+8b+4c=8
81a-27b+9c=63
From: 16a+8b+4c=8, the we have 4a+2b+c=2, or c=-4a-2b+2, we replace c for 2 equations:
9a+6b+4(-4a-2b+2)=-8
9a-3b+(-4a-2b+2)=7
Then
-7a-2b=-16
5a-5b=5, a= b+1
and -7(b+1) -2b =-16
or -9b=-9, b=1, a= b+1=1+1=2, c=-4a-2b+2 = -8-2+2= -8
So the final answer is a= 2, b=1 and c=-8
Hope you understand it.