How do you factor #3x^2 - 19x +6 = 0 #?

1 Answer
George C.
Oct 28, 2016

#0 = 3x^2-19x+6 = (3x-1)(x-6)#

Explanation:

#3x^2-19x+6=0#

Use an AC Method:

Find a pair of factors of #AC=3*6=18# with sum #B=19#

The pair #18, 1# works in that #18+1 = 19# and #18*1 = 18#.

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

#3x^2-19x+6 = 3x^2-18x-x+6#

#color(white)(3x^2-19x+6) = (3x^2-18x)-(x-6)#

#color(white)(3x^2-19x+6) = 3x(x-6)-1(x-6)#

#color(white)(3x^2-19x+6) = (3x-1)(x-6)#

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