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" The 2d line of col. 1 is the 1st line multiplied by 7 in order to render its first term divisible by the first term of the new divisor ; the remainder of the division is the 4th line of col. "
An Elementary Treatise on Algebra: To which are Added Exponential Equations ... - Page 32
by Benjamin Peirce - 1858 - 284 pages
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Elements of Algebra: Including Sturms' Theorem

Charles Davies - Algebra - 1845 - 382 pages
...suppressed in the preceding example, it would be necessary to multiply the whole dividend by this factor, in order to render its first term divisible by the first term of the divisor ; but then, a factor would be introduced into tne dividend which is also contained in the divisor ;...
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A Treatise on Algebra

Elias Loomis - Algebra - 1846 - 376 pages
...divisor, it follows from the above that we may multiply the dividend by any monomial factor which will render its first term divisible by the first term of the divisor. EXAMPLES. Ex. 1. Required tbe greatest common divisor of of + ж3 and x4 — 1. ж3 + ж, first Rem...
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A Treatise on Algebra

Elias Loomis - Algebra - 1846 - 380 pages
...divisor, it follows from the above that we may multiply the dividend by any monomial factor which will render its first term divisible by the first term of the divisor. EXAMPLES. Ex. 1. Required the greatest common divisor of a^ + a;3 and xt — 1. a;5 + 07" x4— 1 5...
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An Elementary Treatise on Algebra

Benjamin Peirce - Algebra - 1851 - 294 pages
...4th line of col. 2, and is used to divide the 1st line of col. 1. The 2d line of col. 1 is the 1st line multiplied by 7 in order to render its first term divisible by the first term of the new divisor ; the remainder of the division is the 4th line of col. 1, which is simplified in the 5th...
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An Elementary Treatise on Algebra: To which are Added Exponential Ewquations ...

Benjamin Peirce - Algebra - 1855 - 308 pages
...4th line of col. 2, and is used to divide the 1st line of col. 1. The 2d line of col. 1 is the 1st line multiplied by 7 in order to render its first term divisible by the first term of the new divisor ; the remainder of the division is the 4th line of col. 1, which is simplified in the 5th...
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A Treatise on Algebra

Elias Loomis - Algebra - 1855 - 356 pages
...first term of the arranged divisor, we may multiply the dividend by any monomial factor which will render its first term divisible by the first term of the divisor. This will not affect the greatest common divisor, because we introduce into the dividend a factor which...
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Elements of Algebra: On the Basis of M. Bourdon, Embracing Sturm's and ...

Charles Davies - Algebra - 1857 - 408 pages
...suppressed in the preceding example, it would be necessary to multiply the whole dividend by this factor, in order to render its first term divisible by the first term of the divisor ; but, then, a factor would be introduced into the dividend which is also contained in the divisor...
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Elements of Algebra: On the Basis of M. Bourdon, Embracing Sturm's and ...

Charles Davies - Algebra - 1860 - 412 pages
...suppressed in the preceding example, it would be necessary to multiply the whole dividend by this factor, in order to render its first term divisible by the first term of the divisor ; but, then, a factor would be introduced into the dividend which is also contained in the divisor...
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New University Algebra: A Theoretical and Practical Treatise, Containing ...

Horatio Nelson Robinson - Algebra - 1863 - 432 pages
...llix'-f- 17x"-f6x— 9 and 4ж'— 18x'+19.ï— 3 ? We first multiply the greater polynomial by 2, to render its first term divisible by the first term of the other polynomial. FIRST OPERATION. 4x4— 24x>+34xa+12a;— 18 4x4— •ISx'+Wx'1— Зх 4a;'—...
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An Elementary Treatise on Algebra: To which are Added Exponential Equations ...

Benjamin Peirce - Algebra - 1864 - 314 pages
...the division is the 4th line of col. 1, which is simplified in the 5th line by the suppression of tho factor 3 a. The 6th line of col. I is the 5th line,...of its leading letter is smaller than that in the first term of the divisor. The remainder arising from the division of the 5th line of col. 1 by the...
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