The factorization of 8x3 - 125 is (2x - 5) (jx2 + kx + 25). What are the values of j and k?

If you would like to find the values of j and k, you can do this using the following steps:

8x^3 - 125 = (2x - 5) * (jx^2 + kx + 25)

8x^3 - 125 = 2jx^3 + 2kx^2 + 50x - 5jx^2 - 5kx - 125

8x^3 = 2jx^3

4x^3 = jx^3

j = 4

2kx^2 + 50x - 5jx^2 - 5kx = 0

2kx^2 + 50x - 20x^2 - 5kx = 0

2kx^2 - 20x^2 + 50x - 5kx = 0

2kx - 20x + 50 - 5k = 0

2x (k - 10) = 5k - 50

2x (k - 10) = 5 (k - 10)

k = 10

The correct result would be: j = 4 and k = 10.