Start with this:
    ____________        
2x-5)18x²-29x-40 
 
2x divided into 18x² gives 9x, so write 9x over the -29x

           9x   
2x-5)18x²-29x-40 
  
Multiply the 9x by the 2x, get 18x², so write 18x² under the 18x²

           9x   
2x-5)18x²-29x-40 
     18x²

Multiply the 9x by the -5, get -45x, so write -45x under the -29x

           9x   
2x-5)18x²-29x-40 
     18x²-45x
 
Draw a line under  the 18x²-45x

           9x   
2x-5)18x²-29x-40 
     18x²-45x
               
Subtract  (18x²-29x)-(18x²-45x) =  18x²-29x-18x²+45x = 16x, so write
16x  under the -45x

           9x   
2x-5)18x²-29x-40 
     18x²-45x
          16x

Bring down the -40 and write it beside the 16x

           9x   
2x-5)18x²-29x-40 
     18x²-45x
          16x-40

2x divided into 16x gives +8, so write +8 over the -40 at the top beside the 9x

           9x+ 8
2x-5)18x²-29x-40 
     18x²-45x
          16x-40

Multiply the +8 by the 2x, get 16x, so write 16x under the 16x

           9x+ 8
2x-5)18x²-29x-40 
     18x²-45x
          16x-40
          16x

 Multiply the +8 by the -5, get -40, so write -40 under the -40.

           9x+ 8
2x-5)18x²-29x-40 
     18x²-45x
          16x-40
          16x-40

Draw a line under the 16x-40

           9x+ 8
2x-5)18x²-29x-40 
     18x²-45x
          16x-40
          16x-40

Subtract  (16x-40)-(16x-40) =  16x-40-16x+40 = 0 so write
0  under the -40

           9x+ 8
2x-5)18x²-29x-40 
     18x²-45x
          16x-40
          16x-40
               0

Since there is a remainder of 0, the correct answer is the
quotient at the top.

Answer: The other factor is 9x+8

Edwin