Find the value of k for (3x⁵ - 4x⁴ + 10x³ + kx² - 8x + 4) that when divided by (x - 2)
gives a remainder of zero.

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

according to egenuity the answer is

step-by-step explanation:

d. 344.22