[tex]a) \ u(x) = 2x^{3}-x^{2}+2x-1 = x^{2}(2x-1) + (2x - 1) = (2x-1)(x^{2}+1)\\\\b) \ u(x) = 8x^{3}-1 = (2x)^{3}-1^{3} = (2x-1)(4x^{2}+2x+1)\\\\c) \ u(x) = 27x^{3}-1 = (3x)^{3}-1^{3} = (3x-1)(9x^{2}+3x+1)\\\\d) \ u(x) = 4x^{3}-3x^{2}+4x-3 = x^{2}(4x-3) + (4x-3) = (4x-3)(x^{2}+1)[/tex]
Wyjaśnienie:
[tex]a^{3}-b^{3} = (a-b)(a^{2}+ab+b^{2})[/tex]
