Answer: The value of the co-efficient 'B' is 9.
Step-by-step explanation: The given trinomial is
\(2x^2+14xy-36y^2 = 2(x + By)(x-2y)~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\)
We are to find the value of co-efficient 'B' in the above factored form.
We need to factorize the given polynomial on the left hand side of equation (i).
The factorization is as follows:
\(2x^2+14xy-36y^2=2(x+By)(x-2y)\\\\\Rightarrow 2(x^2+7xy-18y^2)=2(x+By)(x-2y)\\\\\Rightarrow 2(x^2+9xy-2xy-18y^2)=2(x+By)(x-2y)\\\\\Rightarrow 2\{x(x+9y)-2y(x+9y)\}=22(x+By)(x-2y)\\\\\Rightarrow 2(x+9y)(x-2y)=2(x+By)(x-2y).\)
Comparing both sides of the above equation, we get
B = 9.
Thus, the value of the co-efficient 'B' is 9.
