Question

Exercitiul numarul 5 + cum l-ati facut?

Answer 1

$(x^{2}-3x)( x^{2} -3x+4)+4=[x(x-3)]( x^{2} -3x+4+4) = \\ x( x^{3} -6 x^{2}+13x-12)+4= x^{4}-6 x^{3}+13 x^{2} -12x+4= \\ \frac{(x-1)(x-2)( x^{4}-6 x^{3}+13 x^{2} -12x+4) }{(x-1)(x-2)}= \frac{ x^{3}-4 x^{2} +5x-2 }{x-1} (x-1)(x-2)= \\ x^{2} -3x+2(x-1)(x-2)=(x-1)(x-2)(x-1)(x-2)= \\ (x- 2)^{1+1}(x- 1)^{1+1}=(x- 2)^{2}(x- 1)^{2}$