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[ 4 0 1
-1 -6 -2
5 0 0 ]
\[\lambda ^3+2 lambda ^2 - 29 lambda -30]/

but how do you know to break it into a b c?

how to factorize?
you could try polynomial long division

ugh

\[\lambda^3 +2\lambda^2-29\lambda-30\]

how would you go about doing this?
possibilities: +/- : 1,2,3,5,6,10,30,15

if you plug in -1, you get =0.then what?

your expression does factorizes nicely,
try dividing by \((\lambda+1)\)

i dont know how... i knwo that sounds dumb but how do u do that?

|dw:1341885937030:dw|

|dw:1341885983310:dw|

so\[\lambda^3 +2\lambda^2-29\lambda-30=(\lambda+1)(\lambda^2+\lambda-30)\]

now just factorize the quadratic factor...

thanks. also: do you know about diagnolization?