Factorise the following:

x³ + 2x² + 5x + 10

In the given expression

Check whether there is any common factors for all terms;

None;

Regrouping the 1^st 2 terms we have,

x³ + 2x² = x²[x + 2] -------eq 1

Regrouping the last 2 terms we have,

5x + 10 = 5[x + 2] -------eq 2

Combining eq 1 and 2

x³ + 2x² + 5x + 10 = x²[x + 2] + 5[x + 2]

= [x² + 5][x + 2]

Hence the factors of x³ + 2x² + 5x + 10 are [x² + 5] and [x + 2]