Factories the following expressions

x² + 9x + 18

The given expression looks as

x² + (a + b)x + ab

where a + b = 9; and ab = 18;

factors of 18 their sum

1 × 18 1 + 18 = 19

9 × 2 2 + 9 = 11

6 × 3 6 + 3 = 9

∴ the factors having sum 9 are 6 and 3

x² + 9x + 18 = x² + (6 + 3)x + 18

= x² + 6x + 3x + 18

= x(x + 6) + 3(x + 6)

= (x + 6)(x + 3)

Hence the factors of x² + 9x + 18 are (x + 6) and (x + 3)