Question

How do you factor `45w ^ { 2} + 22w - 3`?

Answer 1

(9ww - 1)(5w + 3)

Explanation:

Use the New AC Method to factor trinomials (Socratic, Google Search)
`f(w) = 45w^2 + 22w - 3 = 45(w + p)w + q)`
Converted trinomial:
`f'(w) = w^2 + 22w - 135 = (w + p')(w + q')`
Find 2 number p' and q', that have opposite signs (ac < 0), knowing the sum (b = 22) and the product (ac = - 135). They are:
p' = -5 and q' = 27 --> Factor pair of - 135. --> (-5, 27)
Back to f(w): `p = (p')/a = - 5/45 = - 1/9` and `q = (q')/a = 27/45 = 3/5`.
Factored form:
`f(w) = 45(w - 1/9)(w + 3/5) = (9w - 1)(5w + 3)`