If on dividing 2x³ + 6x² - (2k - 7)x + 5 by (x + 3), the remainder is k - 1 then the value of k is

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

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

f(x) = 2x³ + 6x² - (2k - 7)x + 5

∴ On dividing f(x) by x + 3 or (x - (-3)), Remainder = f(-3)

Given, remainder = k - 1

∴ f(-3) = k - 1

$\Rightarrow 2(-3)^3 + 6(-3)^2 - (2k - 7)(-3) + 5 = k - 1 \\[0.5em] \Rightarrow -54 + 54 + 6k - 21 + 5 = k - 1 \\[0.5em] \Rightarrow 6k - 16 = k - 1 \\[0.5em] \Rightarrow 6k - k = 16 - 1 \\[0.5em] \Rightarrow 5k = 15 \\[0.5em] \Rightarrow k = 3.$

∴ Option 4, is the correct option.