Zeros: x=1 (multiplicity 2) and x=-4

Starting with x=1, subtract 1 from each side,
(x-1)=0

Our polynomial will have multiplicity of 2 for this particular zero,
(x-1)(x-1)

and do similar with the x=-4, add 4 to each side,
(x+4)=0

So our final result is: (x-1)(x-1)(x+4)

Expand out the brackets if you need this in standard form.