`Delta =|(x,1,0),(x^2,2x+y,1),(0,x+y,2x+3y)|` is not divisible by

If D=|(1, 1, 1), (1, 1+x, 1), (1, 1, 1+y)| for x!=0, y!=0 then D is (1) divisible by neither x nor y (2) divisible by both x and y (3) divisible by x but not y (4) divisible by y but not x

Let Delta(x,y)=|(1,x,y),(1,x+y,y),(1,x,x+y)| Then Delta(-3,2) equals

If x,y,z are different and Delta = |(x, x^2, 1+x^3),(y,y^2,1+y^3),(z,z^2,1+z^3)|= 0 then show that 1 + xyz = 0

If x,y,z are different and Delta=|{:(x,x^2,1+x^3),(y,y^2,1+y^3),(z,z^2,1+z^3):}| =0 then show that 1+xyz=0

If x,y and z are different and Delta=|{:(x,x^2,1+x^3),(y,y^2,1+y^3),(z,z^2,1+z^3):}|=0 then show that 1+xyz=0

If D=|1 1 1 1 1+x1 1 1 1+y|"f o r"x!=0, y!=0 then D is (1) divisible by neither x nor y (2) divisible by both x and y (3) divisible by x but not y (4) divisible by y but not x

If D=|[1, 1, 1], [1, 1+x, 1], [1, 1, 1+y]| for x!=0, y!=0 then D is (1) divisible by neither x nor y (2) divisible by both x and y (3) divisible by x but not y (4) divisible by y but not x

If x,y,z are different and Delta= {:|(x,x^2,1+x^3),(y,y^2,1+y^3),(z,z^2,1+z^3)|=0 , show that xyz=-1

If (-2,1) is the centroid of the triangle having its vertices at (x,0),(5,-2),(-8,y), then x,y satisfy the relation 3x+8y=0 (b) 3x-8y=0( c) 8x+3y=0 (d) 8x=3y