All mathematical problems are decomposed into factors.

Solution:1.3x2-7x-1= [x-(7+radical number 6 1)/6][x-(7- radical number 6 1)/6].

2.4x2-12x+1= [x-(3+2 radical 2)/2] [x-(3-2 radical 2)/2].

3. x 2-4xy+2y 2 = [x-(2+radical number 2)y][x-(2- radical number 2)y]

4.x2+2x-4 =[x-( 1+ radical number 5)][x-( 1- radical number 5)].

5.x2-4x- 1 =[x-(2+ radical number 5)][x-(2- radical number 5)].

6.2x 2+3x- 1 =[x-(-3+ radical number 17)/4][x-(-3- radical number 17)/4].

7.-a 2+5a+2 =-[a-(5+root number 33)/2][A-(5- root number 33)/2].

8.x2+xy-3y 2 =[x-(- 1+ radical number 13)y/2][x-(- 1- radical number 13)y/2]

9.3x 2y 2+ 10xy+5 =[xy-(-5+ radical number 10)/3][xy-(-5- radical number 10)/3].