Question

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

Answer 1

j = 4 and k = 10

Explanation:

Answer 2

D

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