An Elementary Treatise on Algebra: To which are Added Exponential Equations and Logarithms |
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Page 11
... factor by A and of the other by B , and those of their negative terms respectively by C and D ; and , then , the fac ... factor by the positive term of the other , as -C by B or -D by A. Hence , The product of two polynomials is obtained ...
... factor by A and of the other by B , and those of their negative terms respectively by C and D ; and , then , the fac ... factor by the positive term of the other , as -C by B or -D by A. Hence , The product of two polynomials is obtained ...
Page 13
... factors is even ; and it is negative , as in example 10 , when the number of negative factors is odd . 33. Corollary . The ... factor is 12 , and that of the product is 12 + 12 or 24 . 2 Division of Monomials . SECTION V. Division . 35 ...
... factors is even ; and it is negative , as in example 10 , when the number of negative factors is odd . 33. Corollary . The ... factor is 12 , and that of the product is 12 + 12 or 24 . 2 Division of Monomials . SECTION V. Division . 35 ...
Page 14
... factors of the divisor which are ex- plicitly contained in the dividend , and simply indicating the division with regard to the remaining factors of the divisor . Hence , from art . 28 , Suppress the greatest common factor of the nu ...
... factors of the divisor which are ex- plicitly contained in the dividend , and simply indicating the division with regard to the remaining factors of the divisor . Hence , from art . 28 , Suppress the greatest common factor of the nu ...
Page 21
... factors is known , by dividing by the known factor , and the quotient is the other factor . And when a letter occurs as a factor of all the terms of a quantity , it is a factor of the quantity , and may be taken out as a factor , with ...
... factors is known , by dividing by the known factor , and the quotient is the other factor . And when a letter occurs as a factor of all the terms of a quantity , it is a factor of the quantity , and may be taken out as a factor , with ...
Page 22
... factor a " -1 -1 of this remainder is di- visible by ab , the remainder itself is divisible by a — b , and therefore an -b " is also divisible by a - b ; that is , if the proposition is true for any power , as the ( n − 1 ) st , it ...
... factor a " -1 -1 of this remainder is di- visible by ab , the remainder itself is divisible by a — b , and therefore an -b " is also divisible by a - b ; that is , if the proposition is true for any power , as the ( n − 1 ) st , it ...
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Common terms and phrases
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