# Factorise:

• Apr 11th 2009, 06:10 AM
Mr Rayon
Factorise:
-5x^3 + 24x^2 - 36x + 16
• Apr 11th 2009, 06:16 AM
stapel
Quote:

Originally Posted by Mr Rayon
-5x^3 + 24x^2 - 36x + 16

First do the graph in your calculator, so you start your work already having a pretty good idea of where the zeroes are. (Wink)

Then apply the Rational Roots Test to obtain a list of possible whole-number and fractions zeroes. You should get:

. . . . .$\displaystyle \pm\, \frac{1,\, 2,\, 4,\, 8,\, 16}{1,\, 5}$

Since whole numbers are easier, start trying whole-number solutions, such as -1 and +4, by synthetic division.

Once you've found one zero, you can plug the remaining quadratic into the Quadratic Formula to complete the solution.

• Apr 11th 2009, 06:16 AM
Moo
Hello,
Quote:

Originally Posted by Mr Rayon
-5x^3 + 24x^2 - 36x + 16

2 is a root. I don't know why, I just found it :( You've surely been taught some methods for factorising, haven't you ?

Then write it as (x-2)(ax˛+bx+c) and find a,b,c
• Apr 11th 2009, 06:36 AM
Mr Rayon
Quote:

Originally Posted by Moo
Hello,

2 is a root. I don't know why, I just found it :( You've surely been taught some methods for factorising, haven't you ?

Then write it as (x-2)(ax˛+bx+c) and find a,b,c

What do you mean 2 is a root. How does that help me factorise the above. I don't understand. (Crying)

I'm also not sure what the rational root test and synthetic division are. I'll follow the links and see but I'm pretty sure it's not something that we go through in my math classes.
• Apr 11th 2009, 06:48 AM
stapel
Quote:

Originally Posted by Mr Rayon
What do you mean 2 is a root. How does that help me factorise the above. I don't understand.

To learn the relationship between factors and zeroes, try here. (We had assumed that this material had been covered in class before you were required to use the knowledge. Sorry!)

Quote:

Originally Posted by Mr Rayon
I'm also not sure what the rational root test and synthetic division are. I'll follow the links and see but I'm pretty sure it's not something that we go through in my math classes.

If you're not supposed to use the standard methods (and you must not be, or they would have been mentioned in class and in your book), then please reply with the methods that you are supposed to use. We'll be glad to try to help you with whatever non-standard tools or algorithms they've given you, but you'll first need to tell us what they are. (Wink)

Thank you! :D