math

factor.

x^6 - 124 x^3 - 125

x^7 - 8x^4 - 16x^3 + 128

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  1. first one:
    x^6 - 124 x^3 - 125
    = (x^3 + 1)(x^3 - 125)
    now each of those factors as the sum/difference of cubes to get
    (x+1)(x^2 - x + 1)(x+5)(x^2 - 5x + 25)

    the second is a "grouping" kind at the start ...

    x^7 - 8x^4 - 16x^3 + 128
    = x^4(x^3 - 8) - 16(x^3 - 8)
    = (x^3 - 8)(x^4 - 16)
    = (x-2)(x^2 + 2x + 4)(x^2 + 4)(x+2)(x-2)

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