Factories the following expressions

a² + 10a + 24

The given expression looks as

x² + (a + b)x + ab

where a + b = 10; and ab = 24;

factors of 24 their sum

1 × 24 1 + 24 = 25

12 × 2 2 + 12 = 14

6 × 4 6 + 4 = 10

∴ the factors having sum 10 are 6 and 4

a² + 10a + 24 = a² + (6 + 4)a + 24

= a² + 6a + 4a + 24

= a(a + 6) + 4(a + 6)

= (a + 6)(a + 4)

Hence the factors of a² + 10a + 24 are (a + 6) and (a + 4)