Question

Descompuneti in factorii :
X la 4 -x la 2-4x-4

Answer 1

Explicație pas cu pas:

${x}^{4} - {x}^{2} - 4x - 4 =$

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

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

$= (x + 1)[{x}^{2}(x - 1) - 4]$

$= (x + 1)({x}^{3} - {x}^{2} - 4)$

$= (x + 1)({x}^{3} - 2{x}^{2} + {x}^{2} - 2x + 2x - 4)$

$= (x + 1)[{x}^{2}(x - 2) + x(x - 2) + 2(x - 2)]$

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