Advanced Algebra

Cover Advanced Algebra
Advanced Algebra
Arthur Schultze
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(a-6)- 62.
3/~ 4- (a. T)1 66.
AVx ^ ^/a/x ^ ^/-s/a; \ c/- * \ a. - ' \ 6/-' Va? v^ ViC 249. If we wish to arrange terms according to descending powers of x^ we have to remember that the term which does not contain x may be considered as a term containing ^. The powers of x arranged are : a»3 n3- nt nM /y»— 1 /y»— 2 /y, — 3 Ex. 1. Multiply 3a;-i + «-5 by 2x-l. Arrange in descending powers of x.
Check.
If a; = l x_5 + 3x-i = -1 2a;-l = +1 2x2- 10a; + (3 — a; + 5 - -. 3x-i 2x2- llx+ 11 - -3x-i = -
...1 Ex. 2. Divide \/a4_4-v/64-6av^ + 9A/a'&' by 2 ^6^ _ 3 ^^5 _^ ^, at _ 6 a&3 + 9 «%' - 4 6^ «! _3A^ + 2&^ at _ 3 a&^ + 2 a^&^ at _ 3 ah^ - 2 6* - 3 a&^ + 7 Jft* - 4 ftt - 2 a^& 3 4. 6 a^?> -4&t 2a3-63 _)_6a36-4 6a THE THEORY OF EXPONENTS Ex. 3. Find the square root of af — 2x V a + 3 a ^^— -i- — • X x^ Write with fractional and negative exponents : 239 — 2 ah f^ - 2 a% + 3 a - 2 d^x-^ + a'^x-'^ \ x - a^ + ax-^ 2x-a^ 2a^x + Sa 2 a^a; + a 2x-2a^ + 2a -2 a^x-^ + a'^x-^ 2a -2 a^x-i + a'^x'^ This answer may be written without negative and fractional exponents i X — V a -i — EXERCISE 96 Perform the operations indicated : 1.

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