P (x) = 3 (x^2 + 10x + 5) - 5 (x - k) in the polynomial p (x) defined above, k is a constant. if p (x) is divisible by x, what is the value of k?

We have the following polynomial:

P (x) = 3 (x ^ 2 + 10x + 5) - 5 (x - k)

Let's rewrite the polynomial:

P (x) = 3x ^ 2 + 30x + 15 - 5x + 5k

P (x) = 3x ^ 2 + 25x + 15 + 5k

For the polynomial to be divisible by x, then the constant term must be equal to zero:

15 + 5k = 0

Clearing k:

5k = - 15

k = - 15 / 5

k = - 3

Answer:

the value of k is:

k = - 3