Question

Factorise the following:

x² + x(1 + p) + p

Answer 1

Given expression: x² + x(1 + p) + p

Step-wise calculation:

1. Expand the expression:

x² + x(1 + p) + p = x² + x + xp + p

2. Group the terms to factor by grouping:

(x² + x) + (xp + p)

3. Take out common factors from each group:

x(x + 1) + p(x + 1)

4. Factor out the common binomial factor (x + 1):

(x + 1)(x + p)