Given the trinomial, what is the value of the coefficient B in the factored form?

2x2 − 12xy − 32y2 = 2(x − 8y)(x + By)

−4
−2
2
4

B = 2

Step-by-step explanation:

Factor the left side

2x² - 12xy - 32y² ← factor out 2 from each term

= 2(x² - 6xy - 16y²)  

Consider the factors of the coefficient of the y² term (- 16) which sum to give the coefficient of the xy- term (- 6)

The factors are - 8 and + 2, since

- 8 × 2 = - 16 and - 8 + 2 = - 6, thus

x² - 6xy - 16y² = (x - 8y)(x + 2y)

and

2x² - 12xy - 32y² = 2(x - 8y)(x + 2y) ← in factored form

Compare the factored form to the right side

Thus B = 2

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