How do you factor the trinomial #12y^2-13y+3#?

1 Answer
George C.
Sep 14, 2016

#12y^2-13y+3 = (3y-1)(4y-3)#

Explanation:

Given:

#12y^2-13y+3#

Use an AC method:

Look for a pair of factors of #AC = 12*3 = 36# with sum #B=13#

The pair #9, 4# works.

Use this pair to split the middle term, then factor by grouping:

#12y^2-13y+3 = 12y^2-9y-4y+3#

#color(white)(12y^2-13y+3) = (12y^2-9y)-(4y-3)#

#color(white)(12y^2-13y+3) = 3y(4y-3)-1(4y-3)#

#color(white)(12y^2-13y+3) = (3y-1)(4y-3)#

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