Answer: A factor of 6 over a factor of 5
Given the polynomial function f(x) = 5x^5 – x^3 + 3x + 6
In order to get roots, f(x) = 0
Therefore, 5x^5 – x^3 + 3x + 6 = 0
The highest power, n = 5
The coefficient of highest power, p = 5
The constant, q = 6
The ratio of each rational root of a polynomial function is the value q when p=1
In standard form we divide by ‘p’
Giving us, (5x^5 – x³ + 3x + 6)/5 = 0
x^5 – (x^3)/5 + (3/5)x + 6/5 = 0
From the above equation,
The highest power, n = 5
The coefficient of highest power, p = 1
The constant, q = 6/5
Therefore, the ratio of each rational root of the polynomial function is a factor of 6 over a factor of 5