Question

Given the trinomial, what is the value of the coefficient 'B' in the factored form? 2x2 + 14xy − 36y2 = 2(x + By)(x − 2y) B= ____________ Numerical Answers Expected! Answer for Blank 1:

Answer 1

2x^2 + 14xy - 36y^2 = 
= 2(x^2 + 7xy - 18y^2)  = 
= 2 (x + 9y)(x - 2y)

B = 9 

Answer 2

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.