x2 - x10 + x5 - x12 - x3
x2 - 4
Answer: x (x2-x)
f(x) = x6 - 3x g(x) = x2 - 4 f(g(x)) = f(x2 - 4) = (x2 - 4)6 - 3(x2 - 4) = (x2 - 4)6 - 3x2 - 12 = (x12 - 24x10 + 240x8 - 1280x6 + 3840x4 - 6144x2 + 4096) - 3x2 - 12 = x12 - 24x10 + 240x8 - 1280x6 + 3840x4 - 6147x2 + 4084
x2-3x-28
x2 - x10 + x5 - x12 - x3
x12 = (x6)2 = (x2)6 = x2x2x2x2x2x2
x2 - 4
9 - x2 will factor into (3 - x)(3 + x)
Answer: x (x2-x)
f(x) = x6 - 3x g(x) = x2 - 4 f(g(x)) = f(x2 - 4) = (x2 - 4)6 - 3(x2 - 4) = (x2 - 4)6 - 3x2 - 12 = (x12 - 24x10 + 240x8 - 1280x6 + 3840x4 - 6144x2 + 4096) - 3x2 - 12 = x12 - 24x10 + 240x8 - 1280x6 + 3840x4 - 6147x2 + 4084
x2-3x-28
x2-14 does factor but not pretty; it factors to: (x+sqrt14)(x-sqrt14).
x2-x=x(x-1)
x2 + 6x - 2 can not be factored
x2(x3 + 1) is the best you can do there.
x2-9x = x(x-9)