Question

How do you factor `3h^2 + 19h + 20`?

Answer 1

`f(h) = 3h^2+19h+20`

Let's use AC Method, with a twist...

`A=3`, `B=19`, `C=20`

Look for a factorization of `AC=3*20=60` into a pair of factors whose sum is `B=19`.

The pair `B1=4`, `B2=15` works.

Then for each of the combinations `A`, `B1` and `A`, `B2`, divide by the `"HCF"` (highest common factor) to get the coefficients of a factor of `f(h)`...

`(A, B1) = (3, 4)` `("HCF 1")` `rarr` `(3, 4)` `rarr` `(3h+4)`
`(A, B2) = (3, 15)` `("HCF 3")` `rarr` `(1, 5)` `rarr` `(h+5)`

So `f(h) = 3h^2+19h+20 = (3h+4)(h+5)`