How do you factor #7x^2-10x-8#?

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Answer 1 · 2015-06-03T11:46:47

I will use a version of the AC Method...

#A=7#, #B=10#, #C=8#

Look for a pair of factors of #AC=56# whose difference is #B=10#

The pair #B1=4#, #B2=14# works.

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

#(A, B1) = (7, 4) -> (7, 4) -> (7x+4)#
#(A, B2) = (7, 14) -> (1, 2) -> (x-2)#

So #7x^2-10x-8 = (7x+4)(x-2)#