Question

Find the value of m so that 2x-1 be a factor of 2x4 +4x3 -16x2 +10x +m

Answer 1

if 2x-1 is a factor so
2x-1=0
x=1/2
2x4 + 4x3 - 16x2 + 10x + m =0
2(1/2)4 + 4(1/2)3 - 16 (1/2)2 +10(1/2) + m =0
1/8+1/2-4+5+m =0
1+1-32+40+8m/8=0
2-32+40+8m=0×8
42-32+8m=0
10=-8m
m= 10/-8
m=-5/4