Question

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

j = 6 and k = –10
j = 8 and k = 10
j = 4 and k = 25
j = 4 and k = 10

Answer 1

The values of j and k are j = 4 and k = 10.

Explanation:

We first expand (2x-5)(jx²+kx+25):

(2x-5)(jx²+kx+25) = 2jx³ + 2kx² + 50x - 5jx² - 5kx - 125 = 2jx³ + (2k-5j)x² + (50-5k)x -125.

Since these coefficients must correspond to the given coefficients of the cubic, we have that 2j = 8, 2k-5j = 0, and 50-5k = 0. Solving, we find that j=4 and k=10.