Question

Descompuneti in factori:

a) x⁴+x³+2x²+x+1
b) 3x³+2x²-3x-2

Answer 1

$b)3x^3+2x^2-3x-2=3x(x^2-1)+2(x^2-1)=(x+1)(x-1)(3x+2)$
$a)x^4+x^3+2x^2+x+1=x^2(x^2+x+1)+(x^2+x+1)=(x^2+1)(x^2+x+1)$
Aplicatie:Arata ca numarul $k= \frac{5^{5^5}-1}{5^{5^4}-1}$ e compus.