How do you factor #20m^2+13mn+2n^2#?

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Answer 1 · 2015-06-03T06:33:17

#20m^2+13mn+2n^2# is homogeneous in that all of the terms are of degree #2#, so it can be factored like #20x^2+13x+2#,

Use AC Method to factor.

#A=20#, #B=13#, #C=2#

Look for a factorization of #AC=20*2=40# into a pair of factors whose sum is #B=13#.

The pair #B1=5#, #B2=8# works.

Then for each of the pairs #(A, B1)# and #(A, B2)#, divide that pair by the HCF (highest common factor) to get the coefficients of a factor...

#(A, B1) = (20, 5), HCF=5 -> (4, 1) -> (4m+n)#
#(A, B2) = (20, 8), HCF=4 -> (5, 2) -> (5m+2n)#

So #20m^2+13mn+2n^2 = (4m+n)(5m+2)#