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DAVIES' UNIVERSITY ALGEBRA.

USEFUL ONLY

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THOSE WHO STUD Y.

A. S. BARNES AND COMPANY,

NEW YORK AND CHICAGO.

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ENTERED, according to Act of Congress, in the year Eighteen Hundred and Fifty-nine,

BY CHARLES DAVIES,

In the Clerk's Office of the District Court of the Southern District of New York.

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MOST of the Examples on pages 52 and 53 can be solved the process of factoring, and then taking the product of the common factors.

Factoring,

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(7.).

(x + 3) (x − 1), and (x + 3) (x + 2). The G. C. D. is x + 3.

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3xy(x + y), and 3(x + y) (x + y).

The G. C. D. is 3(x + y), or 3x + 3y.

(9.)

Dividing the first by the second, we find a remainder, a(x3 — ax2 — a2x 2a3).

Suppressing a, and dividing the second polynomial by the result, we find for a remainder,

3a2 (x2 + ax + a2).

ppressing 3a, and dividing the preceding remainder by

the result, we find the division exact.

The G. C. D. is x2 + ax + a2.

(10.)

Multiplying the first polynomial by 5, and dividing by the second, we find for the first remainder,

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Multiplying the second polynomial by 16, and dividing by the first remainder, we find for a second remainder,

1252225, or 25(5-1).

Suppressing the factor 25, and dividing the preceding re

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3x(x+2y), 2y(x+2y), and 42(x+2y).

The G. C. D. is x + 2y.

Factoring,

(8.)

3(a + b) (a b), 3(a + b) (a + b), and з(a + b)xy. .. The G. C. D. is 3(a + b).

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(x+3) (x − 3), (x + 3) (x − 6), and (x+3) (x + 8)

... The G. C. D. is x + 3.

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(10.)

(x — 7) (x — 4), and (27) (x — 8).

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(11.)

(x2 — 3) (x2 — 2), (x2 — 3) (x2 - 4), and (22 — 3) (x2 + 5). ... The G. C. D. is x2 3.

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(12.)

Dividing the first by the second, the first remainder is

2x2+8x + 6, or 2(x2 + 4x + 3).

Suppressing the factor 2, and dividing the second polynomial by the result, we find for the second remainder equal to 0. .. The G. C. D. of the first and second polynomials is

x2 + 4x + 3,

or (x+3)(x + 1).

The third polynomial is divisible by x+3, but is not divisible by +1. Hence, the G. C. D. of the three is

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(x + 3) (x + 2) (x + 4) (x − 2), or (x2+ 2x − 8) (x2+ 5x + 6),

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