Question

How do you factor `3x^2 - 9x + 10`?

Answer 1

`3x^2-9x+10` has no proper factors.

To see this note that there are no common factors of the 3 terms of this expression (other than `+-1`); so it can't be simplified in this way.

Second, consider the discriminant of this expression:
`Delta = b^2-4ac`
`=81-120`
`<0`
So `3x^2-9x+10=0` has no real solutions
`rarr 3x^2-9x+10` can not be factored into anything of the form:
`(ax+b)(cx+d)`