x4 + x2 - 42
Let x2 = t, so that x4 = t2
t2 + t - 42 since -42 = 7(-6) and 7 + (-6) = 1, then
t2 + t - 42 = (t - 6)(t + 7) = (x2 - 6)(x2 + 7) By replacing t with x2. So we have,
x4 + x2 - 42 = (x2 - 6)(x2 + 7) = [x2 - (square root of 6)2](x2 + 7) = (x - sq. root of 6 )(x + sq. root of 6)(x2 + 7)
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28 ( x2, x3 and x4)
x5-1 = (x - 1)(x4 + x3 + x2 + 1)
You sure can, here is an example I made up to show you: x4+x2= x2(x2+x) When you factor it out it should look like this because if you multiply it back up (where the exponents will multiply not add) it will equal the primary equation.
(x4 - 16) = (x2 + 4) (x2 - 4) = (x2 + 4) (x + 2) (x - 2)
I assume the x4 is x to the 4th power, and x2 is x², or x squared. The two factors would be: (x + 2)(x - 2)(x² + 3) There are 4 solutions for x: x = 2 x = -2 x = √-3 x = -√-3