# Help!! How to factorise x^3 - 9x^2 + 24x - 30?

• Nov 18th 2012, 12:41 AM
mathhawk
Help!! How to factorise x^3 - 9x^2 + 24x - 30?
Help! How to factorise x^3 - 9x^2 + 24x - 30?(Headbang)

It seems according to the key, 2 roots are imaginary and 1 root is real.
• Nov 18th 2012, 12:52 AM
Prove It
Re: Help!! How to factorise x^3 - 9x^2 + 24x - 30?
Can you find a factor of -30 that makes this expression equal 0?
• Nov 18th 2012, 10:44 AM
BobP
Re: Help!! How to factorise x^3 - 9x^2 + 24x - 30?
It doesn't factorise.
A sketch graph shows that there is a single real root to the right of x = 4,
and a table of values narrows it to between x = 5 and x = 6.
You can get a better approximation if you wish, but you are then into your favourite numerical method.
• Nov 18th 2012, 06:27 PM
Prove It
Re: Help!! How to factorise x^3 - 9x^2 + 24x - 30?
If you MUST try to get the exact real solution, I suggest you read this...
• Nov 19th 2012, 02:10 PM
Re: Help!! How to factorise x^3 - 9x^2 + 24x - 30?
Well if you have something in the form of ax^3+bx^2+cx+d=0 you can try doing synthetic division by x-1 and that will give you (x-1)q(x)+r=0.
• Nov 19th 2012, 03:28 PM
topsquark
Re: Help!! How to factorise x^3 - 9x^2 + 24x - 30?
Quote:

Well if you have something in the form of ax^3+bx^2+cx+d=0 you can try doing synthetic division by x-1 and that will give you (x-1)q(x)+r=0.

And this does what? I don't see where you are headed here.

-Dan
• Nov 19th 2012, 04:41 PM
Soroban
Re: Help!! How to factorise x^3 - 9x^2 + 24x - 30?
Hello, mathhawk!

Quote:

Help! .How to factorise: $f(x) \:=\:x^3 - 9x^2 + 24x - 30\,?$
According to the key, 2 roots are imaginary and 1 root is real.

It is not factorable.

The only possible rational roots are: . $\pm1,\:\pm2,\:\pm3,\:\pm5,\:\pm6,\:\pm10,\:\pm15, \:\pm30$
. . None of them are zeros of the polynomial.

We find that: . $\begin{Bmatrix}f(5) &=& \text{-}10 \\ f(6) &=& +6 \end{Bmatrix}$

Hence, there is a root (irrational) on the interval $(5,\,6).$

Another possibility: a typo in the problem.
. . Could the constant term be -20 or -36?