How do you factor #6x^2 - 11x +3?

1 Answer
Nghi N.
May 16, 2015

#f(x) = 6x^2 - 11x + 3 = (x - p)(x - q)#. Find p and q.

Converted trinomial:# f'(x) = x^2 - 11x + 18 = (x - p')(x - q') #(a.c = 18)

Find p' and q' by composing factor pairs of a.c = 18: (1, 18)(2, 9). This last sum is 11 = -b. Then p' = -2 and q'= -9. We get: #p = (p')/a = -2/6 = -1/3 #and #q = (q')/a = -9/6 = -3/2#.

#f(x) = (x - 1/3)(x - 3/2) = (3x - 1)(2x - 3)#
Check:
#f(x) = 6x^2 - 9x - 2x + 3 = 6x^2 - 11x + 3#. OK

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