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" In the first operation we meet with a difficulty in dividing the two polynomials, because the first term of the dividend is not exactly divisible by the first term of the divisor. But if we observe that the co-efficient 4... "
Elements of Algebra: Tr. from the French of M. Bourdon, for the Use of the ... - Page 26
by Bourdon (M., Louis Pierre Marie) - 1831 - 389 pages
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Elements of Algebra: Tr. from the French of M. Bourdon. Revised and Adapted ...

Charles Davies - Algebra - 1835 - 378 pages
...b, is the greatest common divisor. Here we meet with a difficulty in dividing the two polymonials, because the first term of the dividend is not exactly...is not a factor of all the terms of the polynomial divisor, introduce this factor into the dividend. This gives and then the division of the first two...
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Elements of Algebra

Algebra - 1838 - 372 pages
...-3a —ab + a2 — Hence, — b+a, or a— b, is the greatest common divisor. In the first operation we meet with a difficulty in dividing the two polynomials,...is not a factor of all the terms of the polynomial 462— 5ab+az, and that therefore, by the first principle, 4 cannot form a part of the greatest common...
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Elements of Algebra

Charles Davies - Algebra - 1842 - 368 pages
...+a 2 | — 4i+a oTHence, — i+a, or a — i, is the greatest common divisor. In the first operation we meet with a difficulty in dividing the two polynomials,...is not a factor of all the terms of the polynomial 4i2— and that therefore, by the first principle, 4 cannot form a part of the greatest common divisor,...
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Elements of Algebra: Including Sturms' Theorem

Charles Davies - Algebra - 1845 - 382 pages
...a2 — 46 + 0. Hence, — b + a, or a — b, is the greatest common divisor. In the first operation we meet with a difficulty in dividing the two polynomials,...divisor. But if we observe that the co-efficient 4, is not a factor of all the terms of the polynomial 462 — 5ab + a2, and therefore, by the first principle,...
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An Elementary Treatise on Algebra: Designed to Facilitate the Comprehension ...

Ormsby MacKnight Mitchel - Algebra - 1845 - 308 pages
...divisor. 93. Should we find, in commencing the division of the greater by the less polynomial, that the first term of the dividend is not exactly divisible by the first term of the divisor, it will be because there is some factor in the first term of the divisor not found in the first term...
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The Elements of Algebra Designed for the Use of Schools

John William Colenso - Algebra - 1849 - 262 pages
...If now, having first attended to the directions of ("61), we find, at any step of our process, that the first term of the dividend is not exactly divisible by the first of the divisor, then, in order to avoid fractions in the quotient, we may multiply the whole dividend...
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Arithmetic, algebra, differential and integral calculus, by W. Rutherford ...

Royal Military Academy, Woolwich - Mathematics - 1853 - 476 pages
...be introduced finally as a factor of the greatest common measure. 51. Also if the first term of any dividend is not exactly divisible by the first term of the divisor, it may be made so by multiplying the dividend by the least factor which will avoid fractional quotients....
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Elements of Algebra: On the Basis of M. Bourdon, Embracing Sturm's and ...

Charles Davies - Algebra - 1857 - 408 pages
...Operation. 0. Hence, — 6 + a, or a — 6, is the greatest common divisor. In the first operation we meet with a difficulty in dividing the two polynomials,...divisor. But if we observe that the co-efficient 4, is not a factor of all the terms of the polynomial 462 — 5a6 + a2, and therefore, by the first principle,...
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Elements of Algebra: On the Basis of M. Bourdon, Embracing Sturm's and ...

Charles Davies - Algebra - 1860 - 412 pages
...Second Operation. 0. Hence, — b + a, or a — b, is the greatest common divisor In the first operation we meet with a difficulty in dividing the two polynomials,...divisor. But if we observe that the co-efficient 4, is not a factor of all the terms of the polynomial 462 _ 5ab + ffl2) and therefore, by the first principle,...
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The elements of algebra

John William Colenso (bp. of Natal.) - 1869 - 240 pages
...If now, having first attended to the directions of (61), we find, at any step of our process, that the first term of the dividend is not exactly divisible by the the quotient, we may multiply the whole dividend by such a simple factor, as will make its first term...
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