Question

How do you factor the expression `48g^2-22gh-15h^2`?

Answer 1

(8g + 3h)(6g - 5h)

Explanation:

Consider g as variable and h as a constant, then factor this trinomial:
`f(g) = 48g^2 - 22gh - 15h^2 =` 48(g - p)(g - q)
Use the systematic new AC Method (Socratic Search)
Converted trinomial: `f'(g) = g^2 - 22gh - 720 h^2.=` (g + p')(g + q')
p' and q' have opposite signs because ac < 0.
Compose factor pairs of (-720h^2) with a calculator -->.
...(-15h, 48h)(15h, -48h)(-18h, 40h)(18h, -40h). This sum is (-22h = b).
Then, p' = 18h and q' = -40h. Back to original f(g):
`p = (p')/a = (18h)/48 = (3h)/8` and `q = (q')/a = -40h/48 = -5h/6`
Factored form:
`f(g) = 48(g + (3h)/8)(g - (5h)/6) = (8g + 3h)(6g - 5h)`