Factorise the following quadratic expressions: a) K2 - 11K + 24 b) x2 + 11x + 28

The expression is $K^2 - 8k - 3k + 24$.
Group the terms:

$$(K^2 - 8k) - (3k - 24)$$

Factor out the common factor from each group:

$$K(K - 8) - 3(K - 8)$$

Factor out the common binomial $(K-8)$:

$$(K - 8)(K - 3)$$

The factored expression is $\boxed{(K-8)(K-3)}$.

The expression is $x^2 + 11x + 28$.
We need to find two numbers that multiply to 28 and add up to 11. These numbers are 4 and 7.
Rewrite the middle term using these numbers:

$$x^2 + 4x + 7x + 28$$

Group the terms:

$$(x^2 + 4x) + (7x + 28)$$

Factor out the common factor from each group:

$$x(x + 4) + 7(x + 4)$$

Factor out the common binomial $(x+4)$:

$$(x + 4)(x + 7)$$

The factored expression is $\boxed