How do you factor #7x²-22x+3#?

1 Answer
Nghi N.
May 28, 2016

(7x - 1)(x - 3)

Explanation:

Use the new AC method (Socratic Search).
#y = 7x^2 - 22x + 3 =# 7(x + p)(x + q)
Converted trinomial: #y' = x^2 - 22x + 21 =# (x + p')(x + q')
P' and q' have same sign because ac > 0
Factor pair of (ac = 21) --> (-1, -21) . This sumis -22 = b. Then p' = -1 and q' = -21.
Back to y --> #p = -1/7# and #q = -21/7 = -3#
Factored form: #y = 7(x - 1/7)(x - 3) = (7x - 1)(x - 3)#

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