What is the zeros, degree and end behavior of #y=-2x(x-1)(x+5)#?
Polynomial of third degree
This is very easy: the function is already written in its factorized form. So, if you want to solve
you are asking for a multiplication to be zero. A multiplication is zero if and only if at least one of its factors is zero, so the alternatives are
#-2x = 0 \iff x = 0# #x-1 = 0 \iff x = 1# #x+5 = 0 \iff x = -5#
Just by eyeballing the equation, you can tell this is a polynomial of degree three, since it's the multiplication of three degrees of degree one.
But just to be sure, let's do the actual multiplications:
The end behaviour is a direct consequence of the degree. If we call any polynomial of even degree
Since you have a minus sign in front of the polynomial, the limits will be inverted.