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=(-4)/(3)` must satisfy the equation:

So,
`f((-4)/(3) )=0`

Putting
`x=(-4)/(3)`

We get,

`f((-4)/(3) )=12^3+a((-4)/(3) )-20=0`

`12^3+(-4)/(3) a-20=0`

`(-4)/(3) a=20-12^3=20-1708`

`a=-1708 * (-3)/(4) =1281`

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