Question

How do you factor `5x^4+31x^2+6`?

Answer 1

`5x^4 +31x^2 +6`

`=(5x^2 +1)(x^2 +6)`

Explanation:

`5x^4 +31x^2 +6`

Find factors of `5 and 6` whose products add to `31`

We can see that the largest product that we can find using `5 and 6` is 30, so we will not use smaller factors of `6`

`color(white)(.......)5 and 6`
`color(white)(......)darr" "darr`
`color(white)(.......)5" " 1" "rarr 1 xx1 = 1`
`color(white)(.......)1 " "6" "rarr 5 xx 6 = ul30`
`color(white)(...............................................)31`

The top row is the first bracket and the bottom row is the second bracket. The signs are all positive.

`5x^4 +31x^2 +6`

`=(5x^2 +1)(x^2 +6)`