Question

According to the Rational Root Theorem,-2/5 is a potential rational root of which function?
f(x) = 4x^4 – 7x^2 + x + 25
f(x) = 9x^4 – 7x^2 + x + 10
f(x) = 10x^4 – 7x^2 + x + 9
f(x) = 25x^4 – 7x^2 + x + 4

Answer 1

The rational root theorem basically says that if you divide the factors of the last term by the factors of the leading coefficient, then you'll get a list of all the potential rational roots

For example, let's say we had the polynomial 10x^3 + 4x + 27

The leading coefficient is 10. One factor of 10 is \(\Large {\color{red}{2}}\)
The last term is 27. One factor of 27 is \(\Large {\color{blue}{3}}\)

So a potential rational root is
\[\Large \frac{\color{blue}{\text{factor of last term}}}{\color{red}{\text{factor of first coefficient}}} = \frac{\color{blue}{3}}{\color{red}{2}}\]

Answer 2

Hopefully that example makes sense. If not, then let me know.