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

1 Answer
George C. · Meave60
Jun 2, 2015

#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)#

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