Question

aratati ca x4-5x2+4=(x-1)x(x+1)x(x-2)x(x+2)


ps .. x4 este x la puterea 4
si 5x2 este 5x la puterea 2

Answer 1

$x^{4}-5x^{2}+4=x^{4}-4x^{2}-x^{2}+4=\\x^{2}(x^{2}}-4)+1(x^{2}-4)=(x^{2}-1)(x^{2}-4)\\x^{2}-1=(x+1)(x-1)\\x^{2}-4=(x+2)(x-2)\\(x^{2}-1)(x^{2}-4)=(x-1)(x+1)(x-2)(x+2)$