your question: find
if
now, you have stated that
is a polynomial, I am assuming it is a quadratic polynomial (this dosen't always work though...but school problems are generally that way
)
so let
so
now according to your equation,
(you will get this by expanding and simplifying the above equation)
now you can see that the right hand side has no
in it, so a must be equal to 0 in order to equate it.
if
, the equation shortens to
we know the equation to be true for all values of
so put
, it becomes
put
, it becomes
or
and so
or
so we get
and our function
becomes
.if
,