Question

How do you factor the trinomial `36y^2 + 81y + 45`?

Answer 1

Factor `F(y) = 36y^2 + 81y + 45`

Explanation:

I use the new AC Method to factor trinomials (Socratic Search).
`F(x) = 9f(y) = 9(4y^2 + 9y + 5).` Factor f(y).
`f(y) = 4y^2 + 9y + 5 =` 4(y + p)(y + q)
Since (a - b + c = 0), use the shortcut. The 2 factor are: (x + 1) and (c/a = 5/4)
Factored form: `f(x) = 4(x + 1)(x + 5/4) = (x + 1)(4x + 5)`
Factored form of `F(x) = 9(x + 1)(4x + 5)`