Final answer:
The expression k² + 6k + 8 can be factorised as (k + 2)(k + 4), with the numbers 2 and 4 in the gaps, since they add up to 6 and multiply to 8.
Step-by-step explanation:
To factorise the expression k² + 6k + 8, we are looking for two numbers that multiply to give us the constant term (which is 8) and add up to the coefficient of the middle term (which is 6). Considering the factors of 8, we have 1 and 8 or 2 and 4. The correct pair that adds up to 6 is 2 and 4. Therefore, the expression can be factorised as (k + 2)(k + 4).