Question

How do you factor `40x^2 + 26x - 6`?

Answer 1

Factors are `40(x-(26+2sqrt409)/80)(x-(26-2sqrt409)/80)`

Explanation:

A simple way to factorize `ax^2+bx+c`, one needs to split middle term `bx` in two components, so that their product is `ac`. However, this is not possible in `40x^2+26x−6`, as product `ac` is `-240`, `26x` cannot be split into such set of integers.

Hence one ought to use quadratic formula. For this, let us find the roots of equation `40x^2+26x−6=0` using `(-b+-sqrt(b^2-4ac))/(2a)`

These are `(-26+-sqrt(26^2-4xx40xx(-6)))/(2xx40)` or

`(-26+-sqrt(676+960))/80` or `(-26+-sqrt(1636))/80` or

`(-26+-2sqrt409)/80`

Hence factors are `40(x-(26+2sqrt409)/80)(x-(26-2sqrt409)/80)`