Question

for what value of m is 2x^3+8x^2+11x+m+3 is exactly divisible by 2x-1

Answer 1

2x-1=0
2x=1
x=1/2.
2(1/2)^3+8(1/2)^2+11×1/2+m+3=0
Since it is exactly divisible by 2x-1.
That implies;
2×1/8+8×1/4+11/2+m+3=0
1/4+2+11/2+m+3=0
1+8+22/4+m+3=0
31/4+3+m=0
31+12/3+m=0
43/3+m=0
m= -43/3.
Hope it helps.
Cheers!