Question

How do you simplify `(15n^2 – 5n + 45) ÷ 5`?

Answer 1

`(15n^2-5n+45)-:5 = 3n^2-n+9`

`3n^2-n+9` is of the form `an^2+bn+c`, with `a=3`, `b=-1` and `c = 9`.

This has discriminant:
`b^2-4ac = (-1)^2-4*3*9 = 1-108 = -107`
which is negative, so there are no real values of `n` satisfying `3n^2-n+9=0` and no linear factors with real coefficients.