Consider polynomial [tex]3x^3+5x^2+12x+20.[/tex] Group first two terms and last two terms:
[tex]3x^3+5x^2+12x+20=(3x^3+5x^2)+(12x+20).[/tex]
Terms in first brackets have the common factor [tex]x^2[/tex] and terms in second brackets have common factor [tex]4.[/tex] Then
[tex](3x^3+5x^2)+(12x+20)=x^2(3x+5)+4(3x+5).[/tex]
Now you can see the common brackets [tex]3x+5,[/tex] that gives you
[tex]x^2(3x+5)+4(3x+5)=(3x+5)(x^2+4).[/tex]
Answer: [tex]3x^3+5x^2+12x+20=(3x+5)(x^2+4).[/tex]
