Question

How do you factor `3x^2+ x - 14`?

Answer 1

Factor `y = 3x^2 + x - 14`

Explanation:

`y = 3x^2 + x - 14 =`3(x + p)(x + q)
Converted trinomial `y' = x^2 + x - 42.` = (x + p')( + q')
p' and q' have opposite sign. Factor pairs of (-42) -->...(-2, 21)( -3, 14)(-6, 7). This sum is 7 - 6 = 1 = b. Then, p' = -6 and q' = 7.
Therefor, `p = -6/3 = -2` and `q = 7/3`.
Factored form: `y = 3(x - 2)(x + 7/3) = (x - 2)(3x + 7)`