for what value of a is the polynomial (2x³+ax²+11x+a+3) exactly divisible by (2x-1)?
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let 2x-1==o
x=1\2
p(x)=2x^3+ax^2+11x+a+3
p(1\2)=2×(1\2)^3+a(1\2)^2+11\2+a+3
=1\4+a1\2+11\2+a+3=0
Taking LCM
=(1+2a+22+4a+12)\4=0
=36+6a=0÷4
=a=-36\6
=a=-6
this is your answer
x=1\2
p(x)=2x^3+ax^2+11x+a+3
p(1\2)=2×(1\2)^3+a(1\2)^2+11\2+a+3
=1\4+a1\2+11\2+a+3=0
Taking LCM
=(1+2a+22+4a+12)\4=0
=36+6a=0÷4
=a=-36\6
=a=-6
this is your answer
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