How do you factor #5x^2-18x+9#?

1 Answer
Nghi N.
May 16, 2015

#f(x) = 5x^2 - 18x + 9 = (x - p)(x - q)#
I use the new AC Method for factoring trinomials.

Converted trinomial: #f'(x) = x^2 - 18x + 9 = (x - p')(x - q')# Find p' and q' by composing factor pairs of a.c = 45: (1, 45)(3, 15). This sum is 18 = -b. Then p' = -3 and q' = -15.
We get:# p = (p')/a = -3/5, and q = (q')/a = -15/5 = -3.#

Finally, factored form:
# f(x) = (x - 3/5)(x - 3) = (5x - 3)(x - 3).#

Check by multiplication:
#f(x) = 5x^2 - 15x - 3x + 9 = 5x^2 - 18x + 9# . OK

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