Question

One of the factors of

(2x + 5y)² - 5 (2x + 5y) - 14

1. 2x + 5y - 7
2. 2x + 5y - 2
3. 2x - 5y + 2
4. 2x - 5y + 7

Answer 1

Correct Answer - Option 1 : 2x + 5y - 7

Given 

(2x + 5y)2 - 5(2x + 5y) - 14

Calculation

In order to make factors -5(2x + 5y) can be written as (-7 + 2)(2x + 5y) = -7(2x + 5y) + 2(2x + 5y)

Rewriting the given equation as  

(2x + 5y)² - 7(2x + 5y) + 2(2x + 5y) -14

= (2x + 5y)(2x + 5y -7) + 2(2x + 5y -7)

= (2x + 5y - 7)(2x + 5y + 2)

So, 2x + 5y - 7 is a factor.