x^4 - 1   factor the polynomial completely and find all zeros

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Well, let's see. You start with your expression, x^4 - 1. Since you want to find all zeros, you would make it equal zero, so it would be x^4 - 1 = 0.The easiest thing to do is to factor things out.It would turn out to this:x^4 -1 = 0(x^2 -1)(x^2 +1) = 0(x-1)(x+1)(x^2 +1) = 0Then, so find the zeros, you would set each of those factored expressions equal to zero, and solve for x.x-1=0x = 1x+1 = 0x = -1x^2 + 1 = 0x^2 = -1x = -i, i (this only applies if you're trying to find all zeros, and not just real zeros. Check the problem's wording to make sure.)So your zeros would be -1 and 1. Include -i and i, the imaginary zeros, if needed.