Question

Descompuneti in produs de factori:
(x la puterea a doua + x)(x la puterea a doua + x - 8) + 12

Answer 1

(x²+x)(x²+x-8)+12=
Notam x²+x=a
a(a-8)+12=
a²-8a+12=
a²-6a-2a+12=
a(a-6)-2(a-2)=(a-6)(a-2)=(x²+x-6)(x²+x-2)
x²+x-6=x²+3x-2x-6=x(x+3)-2(x+3)=(x+3)(x-2)
x²+x-2=x²+2x-x-2=x(x+2)-(x+2)=(x+2)(x-1)
Deci ecuatia finala va fi:
(x²+x)(x²+x-8)+12=(x+3)(x-2)(x+2)(x-1)

Answer 2

[tex](x^2+x)(x^2+x-8)+12 \\ Notam \ x^2+x=a =\ \textgreater \ a(a-8)+12=a^2-8a+12 = \\ = a^2-6a-2a+12=a(a-6)-2(a-6)=(a-6)(a-2) \\ Dar \ a = x^2+x =\ \textgreater \ (x^2+x)(x^2+x-8)+12=\\=(x^2+x-6)(x^2+x-2)=(x^2+3x-2x-6)(x^2+2x-x-2)=\\=(x(x+3)-2(x+3))(x(x+2)-(x+2)=\\=(x+3)(x-2)(x+2)(x-1)[/tex]