Question

How do you factor `6y^2 + 11y - 21`?

Answer 1

`y_1=7/6, y_2=-3`

Explanation:

using quadratic formula
`y_1,_2= (-11+-sqrt((-11)^2-4*6*(-21)))/(2*6)`
`=>y_1=(-11+sqrt(625))/12=7/6`
`=>y_2=(-11-sqrt(625))/12=-3`

Answer 2

Factor f(y) = 6y^2 + 11y - 21

Ans: (6x - 7)(x + 3)

Explanation:

I use the new AC Method to factor trinomials (Socratic Search)
f(y) = 6(y + p)(y + q)
Converted trinomial: `y' = x^2 + 11y - 126 =` (y + p')(y + q').
p' and q' have opposite signs. Factor pairs of (-126) --> (-2, 63)(-3, 42)(-6, 21)(-7, 18). This sum is 11 = b. Then p' = -7 ans q' = 18.
Therefor, `p = (p')/a = -7/6` and `q = (q')/a = 18/6 = 3`
Factored form: `y = 6(x - 7/6)(x + 3) = (6x - 7)(x + 3)`