Question

How do you factor the trinomial `20q^2-39qb+18b^2`?

Answer 1

(4a - 3b)(5a - 6b)

Explanation:

Factor: `20a^2 - 39ab + 18b^2`.
Use the new AC Method to factor trinomials (Socratic Search)
Consider a as variable and b as constant. Factor the trinomial:
`y = 20a^2 - 39ab + 18b^2 =` 20(a + p)(a+ q)
Converted trinomial: `y' = a^2 - 39ab + 360b^2 =` (a + p')(a + q')
p' and q' have same sign because ac > 0.
Factor pairs of (ac = 260b^2) --> ..(-10b, -36b)(-15b, -24b). This sum is
-39b. Then, p' = -15b and q' = -24b.
Back to original trinomial y, `p = (p')/a = -(15b)/20 = -(3b)/4`,
and `q = (q')/a = -(24b)/20 = -(6b)/5`
Factored form: `y = 20(a - (3b)/4)(a - (6b)/5) = (4a - 3b)(5a - 6b)`