Question

How do you factor the trinomial `x^2+8xy-36y^2=0`?

Answer 1

Factors of `x^2+8xy-36y^2=0` are `(x+(4-2sqrt13)y)(x+(4+2sqrt13)y)`

Explanation:

Note that the trinomial `x^2+8xy-36y^2=0` is homogeneous function of degree two and hence we can consider it as a quadratic equation.

The discriminant, here is `8^2-4xx1xx(-36)=64+144=208`, and it is not a complete square and hence we will not have rational factors for this equation.

Using quadratic formula `x/y=(-b+-sqrt(b^2-4ac))/(2a)`,

`x/y=(-8+-sqrt208)/2=-8/2+-sqrt(16xx13)/2=-4+-2sqrt13`

Hence factors of `x^2+8xy-36y^2=0` are `(x+(4-2sqrt13)y)(x+(4+2sqrt13)y)`