Question

Sa se descompuna in factori dand factor comun :
a)  x(x+1)+(x+1)²-4(x+1)
b)  (x-2)(3x-7)+(x-2)(4x+2)+4(x+2)

Answer 1

Observam ca x+1-se gaseste de mai multe ori in suma
Daca notam x+1-a
rezulta ca ax + a patrat-4a
=a(x+a-4)
=(x+1)(x+x+1-4)
=(x+1)(2x-3)

Answer 2

a) x(x+1)+(x+1)²-4(x+1)=
(x+1)(x+x+1-4)=(x+1)(2x-3)
b) (x-2)(3x-7)+(x-2)(4x+2)+4(x+2)=
(x-2)(3x-7)+2(x-2)(x+2)+4(x+2)=
(x-2)(3x-7)+2(x+2)(x-2+2)=
(x-2)(3x-7)+2x(x+2)=3x²-7x-6x+14+2x²+4x=
5x²-9x+14