f(x) = 32x^6 - 12x^2 + 40

Question

List all the possible rational roots of the following function.

Answer 1

This follows the rational root test, where we find all possible roots (think of them as x-intercepts, these are also called "zeros"). To do this, we must find the factors of the leading coefficient (the number in front of the leading, or highest power term) and the factors of the constant term. The "rational" part implies a "ratio" of these factors, in other words, we divide the constant factors by the leading coefficient factors:

 

Factors of 32: +/-1, +/-2, +/-4, +/-8, +/-16, +/-32

 

Factors of 40: +/-1, +/-2, +/-4, +/-5, +/-8, +/-10, +/-20, +/-40

 

Possible rational roots = (Factors of 40)/(Factors of 32)

 

As you can see, there will be many answers for this, but this is the strategy!

 

Hope this was helpful!

 

Alex