Question 423330
your trinomial is:


x^2 - 14xy - 51y^2


your factors will be in the form of:


(x-ay) * (x+by)


multiply these factors together and you will get:


x^2 + bxy - axy - aby^2


combine like terms to get:


x^2 + (b-a)xy - aby^2


since your original equation is:


x^2 - 14xy -51y^2, this mans that:


(b-a) must be equal to -14
ab must be equal to 51


it just so happens that if a = 17 and b = 3, then you will get:


x^2 + (3-17)xy - (3*17)y^2 which will become:


x^2 - 14xy - 51y^2


so, you need to make a = 17 and b = 3


the general form of your factors is:


(x-ay) * (x+by)


substitute 17 for a and 3 for b to get:


(x-17y) * (x+3y)


multiply these factors together to get:


x^2 + 3xy - 17xy - 51y^2


combine like terms to get:


x^2 - 14xy - 51y^2


your factors are:


(x-17y) * (x+3y)