When the expression x^2 + bx - 24 is factored completely, the difference of the factors is 11. Find both factors if it is known that b is negative. write the steps on the paper pleas
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The two factors are (x + 3) and (x - 8)

Step-by-step explanation:

The given function is x² + b·x - 24

The difference between the factors = 11

The sign of coefficient b = Negative

Therefore, we have;

The factors as (x - c) and (x + d)

-b = d - c...(1)

d × (-c) = -24...(2)

(x + d) - (x - c) = 11

Which gives;

x + d - x  + c = 11

∴ d + c = 11...(3)

From equation (3), we have;

d = -24(-c) = 24/c

d = 24/c

Substituting the value of d in equation (3) gives;

d + c = 24/c + c = 11

24/c + c = 11

∴ c² + 24 = 11·c

c² + 24 - 11·c = 0

c² - 11·c + 24 = 0

(c - 8)·(c - 3) = 0

c = 8 or 3

From d + c = 11, we have, d = 3 or 8

Given that -b = d - c, therefore c > d and c = 8, d = 3

Therefore, the two factors are (x - 8) and (x + 3).