Question

Given the polynomial f(x)=8x^5−5x^3+3x+4 What one of the following is a possible rational root?
a. 4 / 3
b. 5 / 5
c. 4 / 4
d. 6 / 5

i figured it out its c

Answer 1

Consider the polynomial function of degree m:

$f(x)=ax ^{m}+.....+b$

then if f(x) has a rational root, then that /those rational root/s have the form p/q, where p is a factor of b, the constant term, and q is a factor of a, the leading term.

This is called the Rational Root Theorem, or Rational Root test

in our case, a=8, and b=4

lets check the cases:

a. 3 not a factor of 4

b. 5 not a factor of 4

c. 4 a factor of 4, the other 4 is a factor of 8, so 4/4=1 could be a root,

let's check f(1)=8-5+3+4=10. 

so 1 is not a zero, but it was a candidate for a rational root, according to the theorem.

d. 5 is not a factor of 4



Answer: C