Which of the following factors may be used to find the positive zero of the function f (x) = 2x2 + 8x - 24?

A. (x - 4)

B. (2x - 2)

C. (2x - 4)

D. (2x - 6)

Given f (x) = 2x²+8x-24

One way to find the zeros of this function is by factorizing

Find a pair of numbers that multiplied give the same answer as (2 * - 24) and the same pair of numbers must add up to 8 → The value 2, - 24, and 8 are the coefficients of the given function

The pair of numbers are 12 and - 4

Then we write

f (x) = 2x² + 12x - 4x - 24

f (x) = (2x² + 12x) - (4x + 24)

f (x) = (2x (x+6)) - (4 (x+6)) → There's a common factor (x+6)

f (x) = (x + 6) (2x - 4)

f (x) = 0

(x + 6) (2x - 4) = 0

x + 6 = 0 OR 2x - 4 = 0

x = - 6 OR x = 4/2 = 2

The positive zero is x = 2 and it comes from (2x - 4)

Answer: Option C