# Factorising cubic

1. Jan 23, 2016

### Rumplestiltskin

1. The problem statement, all variables and given/known data
The curve C with equation y = f(x) passes through the point (5, 65).
Given that f'(x) = 6x2 -10x - 12,
a) use integration to find f(x)
b) Hence show that f(x) = x(2x+3)(x-4)

3. The attempt at a solution
I have no problem with this question, except it seems the given function for b) might be wrong or at least not complete.
a) integrated for y = 2x3 - 5x2 - 12x + c
65 = 2(5)3 - 5(5)2 - 12(5) + c
= 200 - 125 - 60 + c = 15 + c.
65 - 15 = 50 = c,
Therefore y = 2x3 - 5x2 - 12x + 50.
b) Taking out x, we get x(2x2 - 5x - 12) + 50.
This factors into x(2x+3)(x-4) + 50. So the given function is missing the +50. My fault or printing error?

2. Jan 23, 2016

### Staff: Mentor

2*53 is not 200.

3. Jan 23, 2016

### Rumplestiltskin

Argh... thanks. I went over that 4 or 5 times and didn't catch it out.

4. Jan 23, 2016

### SteamKing

Staff Emeritus
For future reference, a solitary factor of x implies that the constant term is zero in the full polynomial.