Question

How do you factor `2m^2 - 11m + 15`?

Answer 1

`(m-3)(2m-5)`

Explanation:

Here's a way to do it...
`2m^2-11m+15`
Multiply the squared value with 15
`m^2-11m+30`
Factor normally...
`(m-6)(m-5)`
divide both values by 2
`(m-3)(2m-5)`
5/2 won't be a whole number, so move that number before the `m`

Answer 2

(2m - 5)(m - 3)

Explanation:

Use the new AC Method (Socratic Search)
`f(m) = 2m^2 - 11m + 15 =` a(m + p)(m + q)
Converted trinomial:
`f'(m) = m^2 - 11m + 30 =` (m + p')(m + q')
Find p' and q', knowing the sum (-11) and the product (30).
They are: p' = - 5, and q' = - 6
Back to f(m) --> `p = (p')/a = - 5/2`, and `q = -6/2 = - 3`.
Factored form:
`f(m) = 2(m - 5/2)(m - 3) = (2m - 5)(m - 3)`