Question

The H. C. F. of x² - xy - 2y² and 2x² - xy - y² is:
1. 1
2. x + y
3. 2x - 3y
4. none of these

Answer 1

Correct Answer - Option 1 : 1

Calculation:

Given polynomial,

x² - xy - 2y²

= x² - (2 - 1) xy - 2y²

= x² - 2xy + xy - 2y²

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

= (x - 2y) (x + y)       ....(1)

And, 2x² - xy - y²

= 2x² - (2 - 1)xy - y²

= 2x² - 2xy + xy - y²

= 2x ( x - y) + y(x - y) 

= (2x + y) (x - y)     ....(2)

from equation (1) & (2) 

H.C.F of given polynomial = 1