1. ## Cubic Equation Problem

1) Let f(x) = x^3 - kx^2 +2kx - k - 1
a) Show that f(x) is divisible by x-1, well thats obvious f(1) = 0
but then there is part b - factorise it.
I know how to do it when there is a number, but its confusing when there is a pronumeral, how do i go about this. Specifically the "long division" method.
Also, any tips and hints for when you are solving a worded question?

Cheers

2. Originally Posted by theleontan
1) Let f(x) = x^3 - kx^2 +2kx - k - 1
a) Show that f(x) is divisible by x-1, well thats obvious f(1) = 0
but then there is part b - factorise it.
I know how to do it when there is a number, but its confusing when there is a pronumeral, how do i go about this. Specifically the "long division" method.
Also, any tips and hints for when you are solving a worded question?

Cheers
I can never make the code look good for something like long division, but there is always synthetic division.

-Dan

3. Alternatively you can compare coefficients

$\displaystyle x^3-kx^2+2kx-(k+1) = (x-1)(Ax^2+Bx+C)$

To start you off you can say that: $\displaystyle -C = -(k+1) \rightarrow C = (k+1)$. A is also simple to calculate using the same method