Our function is:
[tex]f(x)=12^3+ax-20[/tex]
Now, if [tex]3x+4[/tex] is a factor of [tex]f(x)[/tex] then [tex]x=\frac{-4}{3}[/tex] must satisfy the equation:
So, [tex]f(\frac{-4}{3} )=0[/tex]
Putting [tex]x=\frac{-4}{3}[/tex]
We get,
[tex]f(\frac{-4}{3} )=12^3+a(\frac{-4}{3} )-20=0[/tex]
[tex]12^3+\frac{-4}{3} a-20=0[/tex]
[tex]\frac{-4}{3} a=20-12^3=20-1708[/tex]
[tex]a=-1708 \times \frac{-3}{4} =1281[/tex]
So, the value of 'a' for the given expression is 1281.
