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

1 Answer
Nghi N.
Apr 12, 2016

(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)#

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