Factorize the expressions and divide them as directed:

(x² + 7x + 12) ÷ (x + 3)

In the given term

Dividend = (x² + 7x + 12)

The given expression looks as

x² + (a + b)x + ab

where a + b = 7; and ab = 12;

factors of 12 their sum

1 × 12 1 + 12 = 13

6 × 2 2 + 6 = 8

4 × 3 4 + 3 = 7

∴ the factors having sum 7 are 4 and 3

x² + 7x + 12 = x² + (4 + 3)x + 12

= x² + 4x + 3x + 12

= x(x + 4) + 3(x + 4)

= (x + 4)(x + 3)

Divisor = (x + 3)

=

= (x + 4)

Hence dividing (x² + 7x + 12) by (x + 3) gives out (x + 4)