Question

What is the factors for `(3x² + 4x + 1)`?

Answer 1

Check for integer solutions first:
Can we find pairs one from each of the sets of factors for 3 and 1 such that the sum of the products of the pairs equals 4?

`3 =color(red)(3)xxcolor(red)(1)`
`1 = color(blue)(1)xxcolor(blue)(1)`
`(color(red)(3)xxcolor(blue)(1))+(color(red)(1)xxcolor(blue)(1)) = 4`

So
`(3x^2+4x+1)`

`= (color(red)(3)x+color(blue)(1))*(color(red)(1)x+color(blue)(1))`