Which one of the following factors does the expansions of the determinant `({:(x,y,3),(x^(2),5y^(2),9),(x^(3),10y^(3),27):})` contain ?

Options

A. x - 3
B. x - y
C. Y - 3
D. x - 3y

Answer

A

Explanation

On Applying
`C_(1) rarr C_(1) - C_(3)`
`|{:(x-3,y,3),(x^(2)-9,5y^(3),9),(x^(3)-27,10y^(5),27):}|`
`(x-3)|{:(" "1,y,3),(x+3,5y^(3),9),(x^(2)+9-3x,10y^(5),27):}|`