ALGEBRA. 1 7 



IV. TJieory of Divisors. 



89. Determine the condition necessary in order that 

 t and 



may have a common divisor of the form x + c, and prove that such 

 a divisor will also be a divisor of px* + (7 p') x q' t 



90. The expression 



y* + Soar 4 + 3te 4- ex* + Zdx* + 3ex +/ 

 will be a complete cube if 



if, / * c -rf =6 _ .. 



V 6a 



91. The expression af-baf+caf+dx-e will be the prx> 

 of a complete square and a complete cube, if 



9<* 50 <** 



92. Prove that o* + bx 4- c, and a + &c 4 -f- ex* will have a 

 common quadratic factor, if 



6V = c- - 



93. The expressions 



ajf + a^ + aft + ajc + a^ and a 4 x 4 + a^ o.^ -t- o,x + <v 

 will have a common quadratic factor. 



(a. - o 4 - eg (a 4 - a/ + (a. - a,) (o.a. - a.aj - 0. 



The expression * + />* + 7* + r will be divisible* 



* -i-ax-t-' 



-^-O, and 6 - 96* + ry6 - r* - 0. 



2 



