Question

10n^3-25n^2-16n+40 I'm so lost on this please help

Answer 1

I think you're factoring this...? You can do that by grouping here.  Put the 4 terms in groups of 2 and factor out the greatest common factor. What's left behind is a common binomial factor that can also then be factored out. Like this:
$(10 n^{3} -25 n^{2})-(16n+40)$
Factoring what we can out of both sets gives us this:
$5 n^{2} (2n-5)-8(2n-5)$
The 2n-5 is a common factor between both the sets of terms, which in turn can also be factored out:
$(2n-5)(5 n^{2}-8)$
I'm not exactly sure what you are doing with this, but we can keep factoring for the sake of completeness.  The 5 n-squared term can also be factored:
$5 n^{2}-8=0$ and $5 n^{2} =8$ and $n^{2} = \frac{8}{5}$ so $n= \frac{ \sqrt{8} }{ \sqrt{5} }$.  Simplifying that down its simplest is this:
$n=+/- \frac{2 \sqrt{10} }{5}$
So your three factors for that polynomial are
$(n- \frac{5}{2} ),(n- \frac{2 \sqrt{10} }{5} ),(n+ \frac{2 \sqrt{10} }{5} )$,