Question

 descompunand in  factori ireductibili :$(x^{2} -9) ^{2} -( x^{2} +7x + 12) ^{2}$

Answer 1

[(x²-9)-(x²+7x +12)][(x²-9)+(x²+7x+12)]=

=(x²-9-x²-7x-12)(x²-9+x²+7x+12)=

=(-7x-21)(2x²+7x+3)=

= -7(x+3)(2x²+7x+3)

a=2
b=7
c=3
Δ= 49-4*2*3= 49 -24=25

x1;x2= (-7 +/- √25)/2*2=  (-7+/- 5)/4

x1=(-7+5)/4= -2/4= -1/2

x2= (-7-5)/4= -12/4= -3

(2x²+7x+3)=(x+1/2)(x+3)= (2x+1)(x+3)

-7(x+3)(2x+1)(x+3)= -7(x+3)²(2x+1)