How do you factor #3z^2+11z-4#?

1 Answer
George C.
Dec 28, 2015

Use an AC method to find a split of the middle term and hence factor by grouping to find:

#3z^2+11z-4 = (3z-1)(z+4)#

Explanation:

Find a split of #AC = 3*4 = 12# into two factors which differ by #B=11#.

The pair #12#, #1# works, so use that to split the middle term, then factor by grouping:

#3z^2+11z-4#

#= 3z^2+12z-z-4#

#= (3z^2+12z)-(z+4)#

#= 3z(z+4)-1(z+4)#

#= (3z-1)(z+4)#

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