find the zeros of the function: f(x)=2x^4 -x^3 +7x^2 -4x -4 ...
f(1) = 0 , after the first try
so x-1 is one of the factors,
by synthetic division we have
(x-1)(2x^3 + x^2 + 8x + 4) , notice we can group the last one
=(x-1)( x^2(2x+1) + 4(2x+1) )
= (x-1)(2x+1)(x^2 + 4)
= 0 for zeros of the function, so
x = 1 , -1/2 , or ±2i