Answer: (x - 4)(x - (i))(x + (i))
Explanation:
This factoring job lends itself well to synthetic division. Looking at the constant term, -4, I came up with several possible roots based upon -4: {±1, ±2, ±4}. I chose +4 as my first trial root. Sure enough, there was a zero remainder, which indicated that 4 is a root of this polynomial and (x - 4) is a factor. The coefficients of the trinomial quotients are 1 0 1, which indicates a quotient of x^2 + 1, which has the following roots: x = +(i) and x = -(i)
So the complete factorization of the polynomial is (x - 4)(x - (i))(x + (i)).
4 ) 1 -4 1 -4
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Answer:
1