SOLUTION: I need your help with, Factoring Trinomials By Grouping, If the Trinomials cannot be factored write "PRIME" 3x^2-7xy+6xy-14y^2

Question 19893: I need your help with, Factoring Trinomials By Grouping, If the Trinomials cannot be factored write "PRIME"
3x^2-7xy+6xy-14y^2
Answer by vidyamanohar(13) (Show Source): You can put this solution on YOUR website!
Probably this question is given half solved.
I guess the real question as to factorize 3x^2-xy-14y^2
The task now is to write the coefficient of xy (here it is -1) as the sum of two numbers whose product is exactly equal to the product of 3 and -14 (the coefficients of x^2 and y^2 respectively)
the numbers we can make out are -7 and 6 as their sum is -1 and product -42, same as the product of 3 and -14!!!
so we can write the given expression as
3x^2+6xy-7xy-14y^2
that gives
3x(x+2y)-7y(x-2y)
=(3x-7y)(x+2y)
Hence the factors are (3x-7y)and (x+2y)
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