Question

How do you factor the trinomial `15m^2 + 19m + 6`?

Answer 1

`(m+2/3)*(m+3/5)`

Explanation:

first make sure the coefficient of `m^2` is 1
you can factorize a quadratic polynomial in the form:
`m^2+`(sum of two numbers)`m+`(product of two numbers)
let the two numbers be `a,b`
so, from the equation, we have
`a+b = 19/15` `&` `a*b = 6/15`

solve this 2 equation 2 unknown by substituting either `a=6/(15b)` or `b=6/(15a)` into the eq `a+b=19/15`
on solving you get the two numbers `a` & `b` as `2/3,3/5`
now, you can write:
`m^2+(2/3+3/5)m+(2/3*3/5)`
`m^2+2/3m+3/5m+(2/3*3/5)`
`m(m+2/3)+3/5(m+2/3)`
`(m+2/3)*(m+3/5)`