Factor 3x squared plus 3x minus 9

Question

factor the polynomial

Answer 1

3x²+3x-9=3(x²+x-3) is the only rational factorisation.

To take it further x²+x-3=(x²+x+¼)-3¼=(x+½)²-(√13/2)², difference of two squares.

This factorises: (x+½+√13/2)(x+½-√13/2) making the complete factorisation:

3(x+½+√13/2)(x+½-√13/2). Note that √13/2 is to be interpreted (√13)/2, NOT √(13/2).