This is a quadratic equation.

When we are asked to facorise a quadratic equation, we should label the 3 parts of it a, b and c.

x² + 10x + 16

a      b        c                   so     a = 1 ,   b = 10 ,   c = 16

Now, we need to find two numbers that  multiply to give c  and  add up to give b.

Go through the numbers that multiply to give 16 in your head, and add them to see if they give 10...

4 x 4 = 16     but does   4 + 4 = 10 ?   No!

16 x 1 = 16   but does  16 +1 = 10?    No!

8 x 2 = 16     but does   8 + 2 = 10 ?   Yes!

Our factorisation is therefore:

x² + 10x + 16  =  ( x + 8 ) ( x + 2 )