The factorization of 8x3 - 125 is (2x - 5) (jx2 + kx + 25). What are the values of j and k? A) j = 6 and k = - 10 B) j = 8 and k = 10 C) j = 4 and k = 25 D) j = 4 and k = 10

j = 4 and k = 10

D

Step-by-step explanation:

8x³ - 125 is a difference of cubes and factors in general as

a³ - b³ = (a - b) (a² + ab + b²)

here 8x³ = (2x) ³ ⇒ a = 2x and 125 = 5³ ⇒ b = 5

8x³ - 125 = (2x - 5) ((2x) ² + (2x * 5) + 5²) = (2x - 5) (4x² + 10x + 25)

compare the coefficients of like terms with jx² + kx + 25

jx² = 4x² ⇒ j = 4 and kx = 10x ⇒ k = 10 → D