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.