An Elementary Treatise on Algebra: To which are Added Exponential Equations and Logarithms |
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Page 27
... greatest com- mon factor or divisor . 57. Problem . To find the greatest common di- visor of several monomials . Solution . It is equal to the product of the greatest common divisor of the coefficients , by those different literal ...
... greatest com- mon factor or divisor . 57. Problem . To find the greatest common di- visor of several monomials . Solution . It is equal to the product of the greatest common divisor of the coefficients , by those different literal ...
Page 28
... find the greatest common divi- sor of any two quantities . Solution . Divide the greater quantity by the less , and the remainder , which is less than either of the given quantities , is , by the preceding article , divisible by the ...
... find the greatest common divi- sor of any two quantities . Solution . Divide the greater quantity by the less , and the remainder , which is less than either of the given quantities , is , by the preceding article , divisible by the ...
Page 29
... Find the greatest common divisor of 1825 and 1995 . Solution . 1995 | 1825 1825 1 1825 | 170 , 1st Rem . * 1700 10 170 | 125 , 2d Rem . 125 1 125 | 45 , 3d Rem . 90 2 45 35 , 4th Rem . 35 1 35 10 , 5th Rem . 30 3 105 , 6th Rem . 10 2 ...
... Find the greatest common divisor of 1825 and 1995 . Solution . 1995 | 1825 1825 1 1825 | 170 , 1st Rem . * 1700 10 170 | 125 , 2d Rem . 125 1 125 | 45 , 3d Rem . 90 2 45 35 , 4th Rem . 35 1 35 10 , 5th Rem . 30 3 105 , 6th Rem . 10 2 ...
Page 30
... Find the greatest common divisor of 13212 and 1851 . Ans . 3 . 3. Find the greatest common divisor of 1221 and 333 . Ans . 111 . 63. The above rule requires some modification in its application to polynomials . Thus it frequently ...
... Find the greatest common divisor of 13212 and 1851 . Ans . 3 . 3. Find the greatest common divisor of 1221 and 333 . Ans . 111 . 63. The above rule requires some modification in its application to polynomials . Thus it frequently ...
Page 31
... Find the greatest common divisor of 6 a2 x3 + 21 a3 x2 27 a5 and 4 x4 +5 a2 x2 + 21 a3 x . Solution . These quantities have no common monomial factor ; but the monomial factor 3 a2 common to all the terms of the first of them , and the ...
... Find the greatest common divisor of 6 a2 x3 + 21 a3 x2 27 a5 and 4 x4 +5 a2 x2 + 21 a3 x . Solution . These quantities have no common monomial factor ; but the monomial factor 3 a2 common to all the terms of the first of them , and the ...
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126 become zero 3d root arithmetical progression coefficient commensurable roots common difference contained continued fraction continued product Corollary deficient terms denote derivative Divide dividend division equal roots equal to zero equation x² factor Find the 3d Find the 4th Find the continued Find the greatest Find the number Find the square Find the sum Free the equation Geometrical Progression given equation given number gives greatest common divisor Hence imaginary roots last term least common multiple letter logarithm monomials multiplied number of real number of terms polynomial positive roots preceding article Problem quantities in example quotient radical quantities ratio real roots reduced remainder required equation required number row of signs Scholium Second Degree Solution Solve the equation square root Sturm's Theorem subtracted Theorem unity unknown quan unknown quantity variable whence