Question

How do you factor the trinomial `3m^2 - m - 30`?

Answer 1

`(3m-10)(m+3)`

Explanation:

First, multiply the coefficient of `m^2` and last term(`-30`)
`3*-30=-90`

Find factors of `-90` that equal the coefficient of `m` when added/subtracted.
`9*-10=-90`
`9-10=-1`

Split `-m` to the factors found above
`3m^2+9m-10m-30`

Factor out the highest common factor of the first two terms, then the last two terms.
`3m(m+3)-10(m+3)`
(your terms in the brackets should be the same to do next step)

Simplify by taking the terms not in the brackets and place them together in a bracket.
`(3m-10)(m+3)`

Answer 2

(m +3)(3m + 10)

Explanation:

You may use the new AC Method to factor trinomials (Socratic Search)
`f(m) = 3m^2 -3 - 30 =` 3(m + p)(m + q)
Converted trinomial:
`f'(m) = m^2 - m - 90 =` (m + p')(m + q')
Find p' and q' knowing the sum (-1) and the product (-90). They are: p' = 9 and q' = -10
Back to f(m) : `p = (p')/a = 9/3 = 3`, and `q = (q')/a = - 10/3`
Factored form:
`f(m) = 3(m + 3)(m - 10/3) = (m + 3)(3m - 10)`
NOTE . This method avoids doing the lengthy factoring by grouping.