Question

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

Answer 1

`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