Final answer:
To determine the value of 'b' when 'x - 4' is a factor of 'x² + bx - 24', we set up the equation (x - 4)(x + a) = x² + bx - 24, solve for 'a', and expand the brackets to find that 'b' equals 2.
Step-by-step explanation:
If x - 4 is a factor of x² + bx - 24, we need to find the value of b.
A factor means that (x - 4) (x + a) = x² + bx - 24, where 'a' is a constant.
Since the constant term when the brackets are expanded will be -4 times 'a', and it needs to be -24, we can say that a = 6.
So now we have (x - 4) (x + 6). Expanding this gives x² + 6x - 4x - 24 which simplifies to x² + 2x - 24. Thus, b must be 2.