Answer:
k = - 14
Step-by-step explanation:
given that (x - 5) is a factor of the polynomial then x = 5 is a root and
x³ - x² + kx - 30 = 0 for x = 5, that is
5³ - 5² + 5k - 30 = 0
125 - 25 + 5k - 30 = 0
70 + 5k = 0 ( subtract 70 from both sides )
5k = - 70 ( divide both sides by 5 )
k = - 14
In this exercise we have to use the knowledge of polynomials to calculate the value of the constant K, in this way we can say that:
k = - 14
Given that the polynomial then x = 5 is a root then we hvae:
[tex]x^3 - x^3 + kx - 30 = 0 \\ 5^3 - 5^2 + 5k - 30 = 0\\ 125 - 25 + 5k - 30 = 0\\ 70 + 5k = 0 \\ 5k = - 70 \\ k = - 14[/tex]
See more about polynomial at brainly.com/question/17822016
