Question

How do you factor `3x^2+7xy+2x^2`?

Answer 1

(3x +y)(x + 2y)

Explanation:

I think the expression to be factored should be:
`f(x, y) = 3x^2 + 7xy + 2y^2. = 3(x + p)(x + q)`
Consider x as variable and y as constant. Factor the trinomial by using the new AC Method (Socratic Search).
Converted `f'(x,y) = x^2 + 7xy + 6y^2= (x + p')(x + q')`
Factor pairs of (ac = 6y^2) --> (1y, 6y). This sum is (7y = b). Therefor,
p' = y and q' = 6y.
Back to f(x,y), `p = (p')/a = y/3` and `q = (q')/a = (6y)/3 = 2y.`

Factored form: `f(x,y) = 3(x + y/3)(x + 2y) = (3x + y)(x + 2y)`