Ross — Verb- Functions. ^ 43 



Hence, if the remainder is to vanish, 



2^(10 - a) = 42, 



and simultaneously 



a^{lO-a) = 147; 



that is, a = 7. Hence 



^ = [/?+10/5- + 42y83+i47^4-|-i3o = [/3 + 7/3'']-' [(3 + 3/3^]'' SO. 



Since R 



(3 + 3/?2' 



its value can be found by division, either by the general method of 

 § 13, or by the artifice usually employed for quadratic equations, 

 namely, 



(3 + 



2a 



1 



2a 



1 



" 2a 

 1 



~ 2a 



so that 



X = [-A-(± a/28/3 + 1 - 1)] i(± v/361 - 1). 



For another example, solve 



+ i2x' + 60^^ - 720:^2 _ |728:r -11 = 0. 



Try division by P + a, so as to produce a quotient of the form 

 (3' + hj3^ + c. 



After the first remainder is found, it will be seen that a must = 2 if 

 the coefficients of (3^ and [3^ in the quotient are to vanish. This gives 

 the exact quotient 



/3«- I6O/33+ 1205, which = - 160/5 + 1205] ; 



so that 



^ = 160^+ 1205]-i0 = (± ^5195 - 80)^ - 2. 



