What are the possible rational roots of f(x) = 5x4 - 173x3 -16x2 -7x -15, according to the rational root theorem? “+-“ means “plus or minus”.

Answer 1

First we identify the "q" and the "p" in the function.

5x⁴ has the highest degree in the function, so q = 5

-15 has the lowest degree (its degree is 0) so p = 15

Next we have to find the factors of "q" and "p." Factors are numbers that you can multiply together to get the original number.

Factors of p = 15: +- 1, +-3, +-5, +-15

Factors of q = 5: +-1, +-5

Now according to the rational root theorem, possible rational roots of zero are +-p/q

Therefore, the possible rational roots of the function are: +-1, +-1/5, +-3, +-3/5, +-5, and +-15