a) $x^{2}$ + 5x + 6
= $x^{2}$ + 2x + 3x + 6
= x ( x+ 2) + 3 (x + 2)
= (x + 3) (x + 2)
..................................................................................
b) $x^{2}$ + 6x + 8
= $x^{2}$ + 2x + 4x + 8
= x ( x+ 2) + 4 (x + 2)
= (x + 2) (x + 4)
.......................................................................................
c) $x^{2}$ - 5x - 14
= $x^{2}$ - 7x + 2x - 14
= x (x - 7) + 2 ( x - 7)
= (x + 2) (x - 7)
.......................................................................................
d) $x^{2}$ - 9x + 18
= $x^{2}$ - 3x - 6x + 18
= x ( x - 3) - 6 (x - 3)
= (x - 6) (x - 3)
.........................................................................................
e) $x^{2}$ - 7x + 12
= $x^{2}$ - 3x - 4x + 12
= x (x - 3) - 4 (x - 3)
= (x - 3) (x - 4)
..........................................................................................
f) 3$x^{2}$ + 9x - 30
= 3 ($x^{2}$ + 3x - 10)
= 3 ($x^{2}$ + 5x - 2x - 10)
= 3 [ x (x +5) - 2 (x+5) ]
= 3 (x - 2) (x +5)
............................................................................................
#HOGWARTS
