Răspuns:
(x²+x)(x²+x-8)+12=(x-1)(x+3)(x-2)(x+2)
Explicație pas cu pas:
(x²+x)(x²+x-8)+12=
=x⁴+x³-8x²+x³+x²-8x+12
=x⁴+2x³-7x²-8x+12
=x⁴-x³+3x³-3x²-4x²+4x-12x+12
=x³(x-1)+3x²(x-1)-4x(x-1)-12(x-1)
=(x-1)(x³+3x²-4x-12)
=(x-1)[x²(x+3)-4(x+3)]
=(x-1)(x+3)(x²-4)
=(x-1)(x+3)(x-2)(x+2)
