Pentru a descompune polinomul
12x² + x - 1
in factori, rezolvam ecuatia atasată.
[tex]12 x^{2} +x-1=0 \\ \\ x_{12} = \frac{-b\; \pm \sqrt{ b^{2}-4ac } }{2a}= \frac{-1\; \pm \sqrt{ 1+4*1*12 } }{2*12}=\frac{-1\; \pm \sqrt{ 49 } }{24}=\frac{-1\; \pm \;7 }{24} \\ \\ x_1=\frac{-1\; + \;7 }{24}= \frac{6}{24} =\frac{1}{4} \\ \\ x_2=\frac{-1\; - \;7 }{24}= \frac{-8}{24} =\frac{-1}{3} \\ \\ \text{Descompunerea este:} \\ \\ 12 x^{2} +x-1=12(x- \frac{1}{4})(x+ \frac{1}{3})[/tex]
