Another way to look at it: the "rational root theorem" says that any rational number roots to a polynomial equation with integer coefficients must be of the form with m, the numerator, a divisor of the leading coefficient, and n, the denominator, a divisor of the constant term. Here, the leading coefficent is 2 which has divisors, 1, -1, 2, and -2, and the constant term is 4 which has divisors 1, -1, 2, -2, 4, -4. The only possible roots of the equation are 1, -1, 2, -2, 4, -4, 1/2, -1/2, 1/4, and -1/4. Putting those numbers into the equation, it is easy to see, immediately, that x= 1 is a root and so x- 1 is a factor. We can continue checking or, by "long division" or "synthetic" division, see that and then see that the last factors as
(I accidently entered "x^^2" rather than "x^2" but instead of getting a usual error message I got "blackisted command". Hope I didn't offend anyone!)