Question

Descompuneți în factori :
a) x²+5x+6=
b) x²-4x-12=
c) (2x-√3)² -27=
d) x²-2x-1-y²=

Answer 1

$a).x^2+5x+6=x^2+3x+2x+6=x(x+3)+2(x+3)= \\ =(x+3)(x+2) \\ \\ b).x^2-4x-12=x^2-6x+2x-12=x(x-6)+2(x-6)= \\ =(x-6)(x+2) \\ \\ c).(2x- \sqrt{3} )^2-27=(2x- \sqrt{3} )^2-3 \sqrt{3} = \\ =(2x- \sqrt{3} -3 \sqrt{3} )(2x- \sqrt{3} +3 \sqrt{3} )=(2x-4 \sqrt{3} )(2x+2 \sqrt{3} )= \\ =2(x-2 \sqrt{3} ) \cdot 2(x+ \sqrt{3} )=4(x-2 \sqrt{3} )(x+ \sqrt{3} ) \\ \\ d).x^2-2x+1-y^2=(x-1)^2-y^2=(x-1-y)(x-1+y)$