x^4 - x^3 + 8x - 8
x^4 - x^3 + 8x - 8
= x^3(x-1) + 8(x-1), grouping
= (x^3+8)(x-1)
= (x+2)(x^2-2x+4)(x-1), using the sum of two cubes formula: a^3+b^3 = (a+b)(a^2-ab+b^2)
x^4 - x^3 + 8x - 8
x^4 - x^3 + 8x - 8
= x^3(x-1) + 8(x-1), grouping
= (x^3+8)(x-1)
= (x+2)(x^2-2x+4)(x-1), using the sum of two cubes formula: a^3+b^3 = (a+b)(a^2-ab+b^2)
You can also combime x^{4} and 8x and x^{3} with 8. You can write
x^{4} -x^{3} +8x - 8 = x(x^{3} +8) - (x^{3} +8) = (x-1)(x^{3} +8) = (x-1)(x+2)(x^{2} -2x +4)