# Factors-4

### From Homeworkwiki

**Factorize :**

**(i) x ^{ 2 } + 5 x + 6**

**(ii) x ^{ 2 } - 5 x + 6**

**(iii) x ^{ 2 } - 5 x - 6**

**(iv) x ^{ 2 } + 5 x - 6**

**Solution :**

(i) **x ^{ 2 } + 5 x + 6** = x

^{ 2 }+ 3 x + 2 x + 6 [Since, 3 + 2 = 5 ; and 3 X 2 = 5]

= x (x + 3) + 2 (x + 3)

= **(x + 3) (x + 2)**

(ii) ** x ^{ 2 } - 5 x + 6**

x ^{ 2 } - 3 x - 2 x + 6 [since, ( -3 ) + ( - 2 ) = - 5 ; and ( - 3 ) X ( - 2 ) = + 6]

= x (x - 3) - 2 (x - 3)

= ** (x - 3) (x - 2)**

(iii) ** x ^{ 2 } - 5 x - 6** = x

^{ 2 }- 6 x + x - 6 [Since, - 6 + 1 = - 5 and, ( - 6 ) X 1 = - 6]

= x (x - 6) + 1 (x - 6)

= **(x - 6) (x + 1)**

(iv) **x ^{ 2 } + 5 x - 6** = x

^{ 2 }+ 6 x - x - 6 [Since, 6 - 1 = 5 and 6 X ( - 1 ) = - 6]

= x (x + 6) - 1 (x + 6)

= **(x + 6) (x - 1)**