If on dividing 4x² - 3kx + 5 by x + 2, the remainder is -3 then the value of k is

1. 4
2. -4
3. 3
4. -3

By remainder theorem, on dividing f(x) by (x - a), the remainder left is f(a).

f(x) = 4x² - 3kx + 5

∴ On dividing f(x) by x + 2 or (x - (-2)), Remainder = f(-2)

Given, remainder = -3

∴ f(-2) = -3

$\Rightarrow 4(-2)^2 - 3k(-2) + 5 = -3 \\[0.5em] \Rightarrow 16 + 6k + 5 = -3 \\[0.5em] \Rightarrow 6k + 21 = -3 \\[0.5em] \Rightarrow 6k = -24 \\[0.5em] k = -4$

∴ Option 2, is the correct option.