Question

How do you factor `11m^2 + 14m -16`?

Answer 1

I will use a version of the AC Method.

Given `f(m) = 11m^2+14m-16`

`A=11`, `B=14`, `C=16`

Look for a factorization of `AC=11xx16=176` into a pair of factors whose difference is `B=14`.

The pair `B1=22`, `B2=8` works.

Then for each of the pairs `(A, B1)` and `(A, B2)`, divide by the HCF (highest common factor) to derive the coefficients of a factor of `f(m)`, choosing signs appropriately...

`(A, B1) = (11, 22) -> (1, 2) -> (m+2)`
`(A, B2) = (11, 8) -> (11, 8) -> (11m-8)`

Hence:

`11m^2+14m-16 = (m+2)(11m-8)`