# How to factor this monster into two quadratics?

1. Mar 23, 2008

### motornoob101

1. The problem statement, all variables and given/known data

How to factor this monster? I am rather clueless
$$144t^{4}-288t^{3}+864t^{2}-720t+900$$

2. Relevant equations

Hint is given that you can get two quadratic polynomials out of it..

3. The attempt at a solution

I can always cheat by using Maple to factor but I don't want do it! I want learn how to do it.

Thanks for any help!

2. Mar 23, 2008

### tiny-tim

Hi motornoob!

Well, for a start, you can divide by 36 to get:

$$4t^{4}\,-\,8t^{3}\,+\,24t^{2}\,-\,20t\,+\,25$$​

hmm … now to think …

3. Mar 23, 2008

### motornoob101

Yeah I divided by 144 to get something smaller but the last number is like 6.25.. I said is no big deal.. but still, I can't factor this.

4. Mar 23, 2008

### tiny-tim

motornoob, there's no point in making fractions - the object is to simplify it!

Stick with mine:
$$4t^{4}\,-\,8t^{3}\,+\,24t^{2}\,-\,20t\,+\,25$$​

I think the best way to do this is just to write it as

$$(at^{2}\,+\,bt\,+\,c)(dt^{2}\,+\,et\,+\,f)\,,$$ ​

and just multiply it out, giving you five equations to solve.

(I've done it - you can more-or-less guess the right answer once you've done that.)

Have a go!

5. Mar 23, 2008

### motornoob101

Five equations to solve huh. I sure hope they don't give us something like this on an exam, considering this part of an integration problem. Thanks so much for the help.