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

Question

sammy [17]

3 years ago

14

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?

Mathematics

1 answer:

musickatia [10] · Answer 1 · 2022-08-04T09:07:53+03:00

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