Question

Descompuneti in factori, grupand convenabil termenii:
a) x³+x²+x+1
b) x³+3x²-x-3
c) x³-2x²-x+2
d) x³-3x²-4x+12

Answer 1

$a) x^{3} + x^{2} +x+1=\ \textgreater \ x^{2} (x+1)+x+1=\ \textgreater \ ( x^{2} +1)(x+1)$
$b) x^{3} +3 x^{2}-x-3=\ \textgreater \ x( x^{2} -1)+3( x^{2} -1)=\ \textgreater \ (x+3)( x^{2} -1)$$=\ \textgreater \ (x+3)(x-1)(x+1)$
$c) x^{3} -2 x^{2} -x+2=\ \textgreater \ x( x^{2} -1)-2( x^{2} -1)=\ \textgreater \ (x-2)( x^{2} -1)$$=\ \textgreater \ (x-2)(x-1)(x+1)$
$d) x^{3} -3 x^{2} -4x+12=\ \textgreater \ x^{2} (x-3)-4(x-3)=\ \textgreater \ ( x^{2} -4)(x-3)$$=\ \textgreater \ (x-2)(x+2)(x-3)$
$Succes$