Question

Descompuneti in factori :
x⁴-18= ?
x⁴-4x+3= ?
x²-6x+6= ?

Answer 1

$x^4-18=(x^2-3\sqrt2)(x^2+3\sqrt2)=(x-\sqrt{3\sqrt2})(x+\sqrt{3\sqrt2})(x^2+3\sqrt2)$

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

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

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

$=(x-1)^2(x^2+x+1+x+1+1)=(x-1)^2(x^2+2x+3)$ ultima paranteza nu se descompune (delta<0).

$x^2-6x+6=x^2-6x+9-3=(x-3)^2-3=$

$=(x-3-\sqrt3)(x-3+\sqrt3)$