DIVISION* 291 



EXAMTLES. 



I. Let it be required to divide <7 ^ — 3a * Af— 3«;v * -j-.v ^ 



— 4a^X-^2^^^ ^^^^ dividual. 



——4a * X- — ^ax * 



-j- ax^ -{-N^ second dividual. 

 -j- ax' -{-x^ 



2. Divide 



* The process may be explained thus ; 



First, a^ divided by a gives a* for the first term of the quo^ 

 tient, by which v\'e multiply the whole divisor, viz. a-\^x, and 

 the product is «- -^a^x, which, being taken from the two first 

 terms of the dividend, leaves — 4^*^ ; to this remainder we 

 bring down — ^ax^, the next term of the dividend, and the sum 

 is — ^^x — $ax^, the first dividual ; now dividing — 4«^.v, the 

 first term of this dividual, by a, the first term of the divisor, there 

 comes out — ^ax, a negative quantity, which we also put in the 

 quotient ; and the whole divisor being multiplied by it, the prod- 

 uct is —-^.a'^x — 4flx^, which being taken from the first dividual, 

 the remainder is -^-ax^ ; to which we bring down x^ , the last 

 term of the dividend, and the sum is +^7a;^ -}-*.% the second di- 

 vidual ; and -^-ax^, the first term of the second dividual, divid- 

 ed by a, the first term of the divisor, gives x^ for the last term 

 of the quotient ; by which we multiply the whole divisor, and 

 the product is -}-«>;* -|-x', which being taken from the second di- 

 vidual leaves nothing ; and the quotient required is n^ — ^^ax^x"^. 



