Question

when a poly is divded by 3x-4, the qoutient is x2-x-4 and the remaider is -9. the poly functions is ?

Answer 1

let f(x) and g(x) be two polynomial functions
q(x) and r(x) will be the quotient and remainder respectively

dividing f over g gives us

\[\Large \frac{f(x)}{g(x)} = \text{Quotient} + \frac{\text{Remainder}}{g(x)}\]

Answer 2

we don't know f(x)
we know g(x) = 3x-4

the quotient is q(x) = x^2-x-4
the remainder is r(x) = -9

\[\Large \frac{f(x)}{g(x)} = \text{Quotient} + \frac{\text{Remainder}}{g(x)}\]
\[\Large \frac{f(x)}{g(x)} = q(x) + \frac{r(x)}{g(x)}\]
\[\Large \frac{f(x)}{3x-4} = x^2-x-4 + \frac{-9}{3x-4}\]

do you see how to isolate f(x) from here?