How do you factor #3y^2+7y-20#?

1 Answer
Nghi N.
Jun 3, 2015

#f(y) = 3y^2 + 7y - 20 #= 3(x - p)(x - q). I use the new AC method

Converted #f'(y) = y^2 + 7y - 60.# a and c have different signs. Compose factor pairs of (a.c = -60) --> (-3, 20)(-4, 15)(-5, 12). This sum is 7 = b. Then p' = -5 and q' = 12.
Back to f(y) -> #p = -5/3 and q = 12/3 = 4.#

Factored form #f(y) = 3(y - 5/3)(y + 4) = (3y - 5)(y + 4).#

Check by developing: #f(y) = 3y^2 + 12 y - 5y - 20.#.OK

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