Factorise and solve the quadratic equations below.

x^2+11x+24=0

X² + 11x + 24 = 0

24*1 = 24

We think of 2 numbers that multiply to give 24 and add up to give 11

The 2 numbers are 8 and 3.

8*3 = 24      and  8 + 3 = 11

So the 11x in    x² + 11x + 24 = 0

Replace 11x with (3x + 8x)

 x² + 11x + 24 = 0

x² + 3x + 8x + 24 = 0            Factorize.

x(x + 3) + 8(x + 3) = 0

(x + 3)(x + 8) = 0

That means:

x + 3 = 0    or  x + 8 = 0

x = 0 - 3                x = 0 - 8

x = -3        or        x = -8

Therefore:  x² + 11x + 24 = 0  is (x + 3)(x + 8) = 0   and x = -3 or x = -8

Hope this helps.