x^5+4x^3-17x+12
(1)^5+4(1)^3-17(1)+12
1+4-17+12=0
x-1 is a factor
(-1)^5+4(-1)^3-17(-1)+12
-1-4+17+12=24
x+1 is not a factor
(1/2)^5+4(1/2)^3-17(1/2)+12
1/32+4(1/8)-17/2+12
1/32+1/2-17/2+12
2x-1 is not a factor
(-3/2)^5+4(-3/2)^3-17(-3/2)+12
(-243/32)+4(-27/8)+51/2+12
-243/32-27/2+51/2+12=525/32
2x+3 is not a factor