Find the value of k for which (x-1) is a factor of

Let, f(x) = 2x³ + 9x² + x + k

Now, we have

x – 1 = 0

x = 1

Hence,

f(1) = 2 × 1³ + 9 × 1² + 1 + k

= 2 + 9 + 1 + k

= 12 + k

As per the question,

(x – 1) is the factor of f(x)

Now, by using factor theorem we get

(x – a) will be a factor of f(x) only if f(a) = 0 and hence f(1) = 0

So,

f(1) = 0

0 = 12 + k

k = -12