Question

Descompuneti in factori:
a) $x^{4}+2a x^{3} -a^{4}-2a^{3}x$
b) $x^{4}+2a x^{3} -a^{4}-2a^{3}x \\ x^{2}-xy-2y-4$
c)$(x+3)^{3}-x-3$
d)$x^{4}-2 x^{3}+2 x^{2}-2x+1$

Dau 20 de puncte+coroana

Answer 1

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Answer 2

a)  (x⁴- a⁴) + 2ax( x²-a²) = ( x² -a²) ( x²+a² ) +2ax ( x² -a²) =
= ( x² -a²) ( x² +2ax +a²) = (x-a) ( x+a) ( x+a)²
b) ( x² -4) -xy -2y= ( x-2) ( x+2) - y ( x+2) = ( x+2 ) ( x-2 -y)
c) (x+3)³ - ( x+3) = ( x+3) ( x²+6x +9-1 ) = ( x+3) ( x² +6x+8)=(x+3)(x+2)(x+4)
d) x⁴ -2x³ +x² +x² -2x +1 = x² ( x² -2x +1 ) + ( x² -2x +1) =
= x²( x-1)² + ( x- 1)²= ( x-1)² ( x² +1)