Factories the following expressions

p² – 10p + 21

The given expression looks as

x² + (a + b)x + ab

where a + b = -10; and ab = 21;

factors of 21 their sum

-1 × -21 -1-18 = -19

-7 × -3 -7-3 = -10

∴ the factors having sum -10 are -7 and -3

p² + 9p + 18 = p² + (-7-3)p + 21

= p² -7p-3p + 21

= p(p-7) -3(p-7)

= (p-7)(p-3)

Hence the factors of p² + 9p + 18 are (p-7) and (p-3)