Answer:
k = -25
Step-by-step explanation:
solving by function and roots
let f(x) = 3x⁵ - 4x⁴ + 10x³ + kx² - 8x + 4
given that when divided by (x-2), the remainder is zero, hence we can say that (x-2) is a factor of f(x), which also means that (x - 2) = 0 or x = 2 is a root of f(x)
recall if we substitute a value of x into f(x) that is a known root of a function, the functions becomes zero,
i.e substitute x = 2 into f(x)
f(2) = 3(2)⁵ - 4(2)⁴ + 10(2)³ + k(2)² - 8(2) + 4 = 0
3(32) - 4(16) + 10(8) + k(4) - 8(2) + 4 = 0
96 - 64 + 80 + 4k - 16 + 4 = 0
100 + 4k = 0
4k = -100
k = -25
