How do you factor #3x^2 - 10x + 3?

1 Answer
Nghi N.
May 9, 2015

I use the new AC Method (Google, Yahoo Search) to factor:
#f(x) = 3x^2 - 10x + 3 = (x -p)(x - q)#
Converted trinomial: #f'(x) = x^2 - 10x +9 = (x - p')(x - q') #with ac = 9
Find p' and q'. Compose factor pairs of ac = 9. Proceed: (1, 9). This last sum is 1 + 9 = 10 = -b then

#p' = -1 -> p = (p')/a = -1/3#
#q' = -9 -> q = (q')/a = -9/3 = -3#

Factored form: f(x) = (x - 1/3)(x - 3) = (3x -1)(x - 3).

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