6. Find the greatest common divisor of 6 ar* — a:- — 5 a; and
21 aj»-26a;«+ 5a:.
The quantities have the common monomial factor x ; remov-
ing it, we find the greatest common divisor of 6 a:* — x — 5 and
21 a:^ — 26 a; + 5. We multiply the latter by 2, to avoid a frac-
tion as the first term of the quotient, giving 42 a;^ — 52 aj + 10.
6aj«-a;-5)42aj»-52a; + 10(7

42x»- 7a;-35



— 45 a: + 45



Dividing by — 46, a; — l)6a;*— a: — 6(6ar + 5

6 a:* — 6 a;



bx — 6
6a; — 5



LEAST COMMON MULTIPLE. 61

Hence, as — 1 is the greatest common divisor of 6 »* — aj — 6
and 21 a:* — 26 a; + 5. Multiplying by x, the common mo-
nomial factor, we obtain a; (x — 1) or a:^ — a; as the required
greatest common divisor, Aris.
EXAMPLES.
Find the greatest common divisors of the following :

6. 6a;* — 7a; — 24andl2a;«H-8aj-16.
7. 24a;«+lla;-28and40a;«-61a; + 14.
8. 2x«-2a;2-3a;H-3and2a;»-2a;2-6a;-h5.
9. 6a;* — 13a; — 28andl5a;2 + 23a; + 4.
10. 8a;*-22a;H-5and6x*-23a; + 20.
IL 5a;«H-68a; + 33andl0a;''^-f 41x + 21.
12. a;»H-2a;* + a; + 2anda;*-4a;«-a;-2.
13. 2a;» — 3x* — a; + land 6a;* — a;* + 3a;-2.
14. X* — x«-f-2a;* + a; + 3anda;*-|-2a;» — a;— 2.
15. a' — 5 a X -h 4 X* and a' — a* x + 3 a x* — 3 x'.
16. X* — x*-5x« + 2x-h"6andx* + x»-x*-2x — 2.
17. 6x^y-\-4:Xi/-2i/ and 4x» + 2x*y-2x2/*.
18. 2 a* + 3 a»x — 9 a*x* and 6 «»- 17 a*x + 14 ax*- 3x«.
