Question

In the expression below, a is an integer. 12^3+ax-20 if 3x+4 is a factor of the expession above, what is the value of a

Answer 1

Our function is:

$f(x)=12^3+ax-20$

Now, if $3x+4$ is a factor of $f(x)$ then $x=\frac{-4}{3}$ must satisfy the equation:

So, $f(\frac{-4}{3} )=0$

Putting $x=\frac{-4}{3}$

We get,

$f(\frac{-4}{3} )=12^3+a(\frac{-4}{3} )-20=0$

$12^3+\frac{-4}{3} a-20=0$

$\frac{-4}{3} a=20-12^3=20-1708$

$a=-1708 \times \frac{-3}{4} =1281$

So, the value of 'a' for the given expression is 1281.