F(x, y) = 5xyf(x, y) = 5xy(5y^2 - 17 x^2y + 6x^4).F(x,y)=5xyf(x,y)=5xy(5y2−17x2y+6x4).
Factor f(x, y) by considering y as variable and x as constant.
Use the new AC Method to factor trinomials (Socratic Search).
f(x, y) = 5y^2 - 17x^2y + 6x^4 =f(x,y)=5y2−17x2y+6x4= 5(y + p)(y + q)
Converted trinomial: f'(x, y) = y^2 - 17x^2y + 30x^4 = (y + p')(y + q')
p' and q' have same sign because ac > 0.
Factor pairs of (ac = 30x^4) --> (-2x^2, -15x^2). This sum is -17x^2 = b. Therefor, p' = -2x^2 and q' = -15x^2.
Back to original f(x, y) --> p = (p')/a = -(2x^2)/5 and
q = (q')/a = -(15x^2)/5 = -3x^2
Factored form of f(x) = 5(y - (2x^2)/5)(y - 3x^2) = (5y - 2x^2)(y - 3x^2)
F(x) = 5xy.f(x) = 5xy(y - 2x^2)(y - 3x^2)
