Question

Can somebody explain how I find the potential roots of this function?

p(x) = x^4 + 22x^2 – 16x – 12

Answer 1

Rational root theorem. Find all the factors of the leading term's coefficient and the constant term; these are 1 and -12, respectively.

1 has only one factor: 1 (call this
`n`)

-12 has a few more:
`\pm1,\pm2,\pm3,\pm4,\pm6,\pm12` (call these
`m`)

Potential roots will take on the form
`\frac mn`, which means you can check these as possible roots:
`\pm1,\pm2,\pm3,\pm4,\pm6,\pm12`

Plug each of these into
`p(x)`. If
`p\left(\frac mn\right)=0`, then
`\frac mn` is a root.

Unfortunately, you'll find none of these work, so this polynomial doesn't have any rational roots (which means finding any could be very tough).