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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?

Respuesta :

carlosego
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
abidemiokin

The value of k if the given polynomial is divisible by x is -3

Given the polynomial function expressed as P(x) = 3(x^2 + 10x + 5) - 5(x - k)

First, we need to expand the given function as shown:

[tex]P(x)=3(x^2 + 10x + 5) - 5(x - k)\\P(x)=3x^2+30x+15-5x+5k\\P(x) = 3x^2+30x-5x+15+5k[/tex]

For the given polynomial to be divisible by x, the constant term of the expression must be zero to have:

[tex]15+5k=0\\15=-5k\\k=-\frac{15}{5} \\k=-3[/tex]

Hence the value of k if the given polynomial is divisible by x is -3

Learn more here: https://brainly.com/question/12472185

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