Factorize the expressions and divide them as directed:

(p² + 5p + 4) ÷ (p + 1)

In the given term

Dividend = (p² + 5p + 4)

The given expression looks as

x² + (a + b)x + ab

where a + b = 5; and ab = 4;

factors of 4 their sum

1 × 4 1 + 4 = 5

2 × 2 2 + 2 = 4

∴ the factors having sum 5 are 4 and 1

(p² + 5p + 4) = p² + (4 + 1)p + 4

= p² + 4p + p + 4

= p(p + 4) + 1(p + 4)

= (p + 1)(p + 4)

Divisor = (p + 1)

=

= (p + 4)

Hence dividing (p² + 5p + 4) by (p + 1) gives out (p + 4)