1. ## cubic polynomial

The cubic polynomial $\displaystyle f(x)$is such that the coefficient of $\displaystyle x^3$ is $\displaystyle 1$ and the roots of $\displaystyle f(x) = 0$ are $\displaystyle k$, $\displaystyle 2k$ and $\displaystyle (1 - k)$, where $\displaystyle k > 0$. It is given that $\displaystyle f(x)$ has a remainder of $\displaystyle 30$ when divided by (x - 1).
Show that $\displaystyle 2k^3 - 3k^2 + k - 30 = 0$
I do not quite understand the question so I don't know where to start from.
I only know that $\displaystyle f(1) = 30$
Does 'root' here mean factor?
Would that mean that $\displaystyle f(x) = (k)(2k)(1 - k)$? But that doesn't make much sense to me because I don't see how $\displaystyle 2k^2 - 2k^3$ has any connection with anything.

I'm sorry for the silly question and any help would be really really appreciated. Thank you in advance.

2. Originally Posted by caramelcake
I do not quite understand the question so I don't know where to start from.
I only know that $\displaystyle f(1) = 30$
Does 'root' here mean factor?
Would that mean that $\displaystyle f(x) = (k)(2k)(1 - k)$? But that doesn't make much sense to me because I don't see how $\displaystyle 2k^2 - 2k^3$ has any connection with anything.

I'm sorry for the silly question and any help would be really really appreciated. Thank you in advance.
$\displaystyle f(x)=(x-k)(x-2k)(x-(1-k))$

CB

3. Thank you! The question is surprisingly simple now