The correct option is C (x−3)(x+8)
In order to factorize x2+5x−24, we need to split the middle term 5x such that the sum or difference is 5 and product is -24.
Hence 5x is split as −3x and 8x.
x2−3x+8x−24
x(x−3)+8(x−3)
Taking out (x−3) common,
x2+5x−24 = (x−3)(x+8).