Factoring polynomials is a matter of making educated guesses. In some cases the educated guesses come easily in others it is not so easy a task.
For our polynomial, let us first factor out 4. Doing this gets is
[tex]-4(y^2+8y-20)[/tex]And now we take a guess at the factors of the polynomial in the parenthesis.
Now remember that,
[tex](y+a)(y+b)=y^2+(a+b)y+ab[/tex]Comparing this with our polynomial suggests
[tex]a+b=8[/tex][tex]ab=-20[/tex]meaning the sum of a and b is 8 and the product is -20. What two numbers could satisfy this condition?
Let us take a guess at a = 10 b = -2. This will give
[tex]-4\textcolor{#FF7968}{\lbrack}(y+10)(y-2)\textcolor{#FF7968}{\rbrack}[/tex]Let us see if this guess works by expanding what is in the square brackets.
[tex]\textcolor{#FF7968}{(y+10)(y-2)}=y(y-2)+10(y-2)=y^2-2y+10y-20[/tex][tex]=\textcolor{#FF7968}{y^2+8y-20}[/tex]which is exactly the same!
Hence, the factorization of - 4y2 - 32y + 80 is
[tex]-4(y+10)(y-2)\text{.}[/tex]