Question

Se considera Polinomul f=x^4+mx^2+2
Pt m=3 descompuneti polinomul in factori ireductibili in R[x]

Answer 1

   
[tex]\displaystyle\\ f=x^4+3x^2+2 =\\\\ =x^4+2x^2+ x^2+2 =\\\\ =x^2(x^2+2)+(x^2+2) =\\\\ =(x^2+2)(x^2+1)\\\\ \Longrightarrow~~f =(x^2+2)(x^2+1)\\\\ \text{unde} (x^2+2)~\text{ si }~(x^2+1)~\text{sunt factori ireductibili in R.} [/tex]

Answer 2

x^4+3x²+2=x^4+x²+2x²+2=x²(x²+1)+2(x²+1)=(x²+1)(x²+2)