Factor completely y^4+3y^3-5y^2-15y

y^4+3y^3-5y^2-15y

First we
will group the first two terms and the last two terms
together:

==> ( y^4 + 3y^3) - ( 5y^2 +
15y)

Now we will factor y^3 from the first two
terms:

==? y^3( y + 3) - (5y^2 +
15y) 

Now we will factor 5y from the last two
terms:

==> y^3 ( y+ 3) - 5y( y +
3)

Now we notice that both terms have  ( y+ 3) , then we will factor
( x+ 3) again:

==> (y+3) ( y^3 -
5y)

Now we will factor y from (y^3 -
5y)

==> (y+3)* y( y^2 - 5)

Now
we can factor (y^2-5) at follows:

(y^2-5) = (
y-sqrt5)(y+sqrt5)

Then the last form
is

(y^4+3y^3-5y^2-15y
= y*(y+3)*(y-sqrt5)(y+sqrt5)