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let p(x)=2x³-ax²-8x+b
if 2x-1 is a factor of p (x)
x=1/2
p(1/2)=2(1/2)³-a(1/2)²-8(1/2)+b
=2/8-a/2-8/2+b
=2/8-a/2-4+b
=1/4-a/2-4+b
=1-16/4-a/2+b
=15/4-a/2+b
p(1/2)=0
15/4-a/2+b=0
-a/2=-15/4-b
-a/2=-(15/4+b)
a=2(15/4+b)
a=30/4+2b
a=15/2+2b say 1
if x+2 is factor
p(-2)=2*-2³-a-2²+16+b
=-16-4a+16+b
=-4a+b
p(-2)=0
-4a+b=0
b=4a say 2
putting value of a in 2
b=4(15/2+2b)
b=30+8b
8b-b=-30
7b=-30
b=-30/7
putting value of b in 1
15/2+2*-30/7
=15/2-60/7
=105-60/7
=45/7
hope this helps you
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