Factor f(t) completely.

Question

f(t)= -t⁴+44t³-612t²+2592t

 

Factor f(t) completely

 

(Please help me with the steps as well, please don't just write the answer)

Answer 1

Okay, this is a crazy problem. If you haven't done polynomial division or synthetic division, I'm not sure how best to tackle this. It does not factor by standard grouping techniques, so synthetic division seems like the way to go. It could be that you're only intended to do the first step.

 

The first step is easy though: find the greatest common factor of all the terms and factor it out. In this case, all the factors have a t, and the leading term is negative, so I'll factor out -t:

 

-t (t³ - 44t² + 612t - 2592)

 

This cubic factor is a beast. For synthetic division, you need to look at the factors of 2592 and see which ones might divide the polynomial evenly.

 

A partial list of factors of 2592, which could be either positive or negative:

1, 2, 4, 6, 8, 9, 12, 18, 24, 27, 32 ...

 

Ugh. Having used a math tool to factor this, I'll give you one for free: one of the roots is 18.

 

Hopefully this helps!