An Elementary Treatise on Algebra: To which are Added Exponential Equations and Logarithms |
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Page 14
To which are Added Exponential Equations and Logarithms Benjamin Peirce. Division of Monomials . SECTION V. Division . 35. Problem . To divide one monomial by , an- other . Solution . Since the dividend is the product of the divisor and ...
To which are Added Exponential Equations and Logarithms Benjamin Peirce. Division of Monomials . SECTION V. Division . 35. Problem . To divide one monomial by , an- other . Solution . Since the dividend is the product of the divisor and ...
Page 15
... DIVISION . 15 Division of Monomials . When the divisor and dividend are both affected by the same sign , the quotient is positive ; but when they are affected by contrary signs , the quotient is negative . Thele for the signs in both ...
... DIVISION . 15 Division of Monomials . When the divisor and dividend are both affected by the same sign , the quotient is positive ; but when they are affected by contrary signs , the quotient is negative . Thele for the signs in both ...
Page 16
... . a - 11b - 18-1a - 11b - 1 . Ans . 3 a - 1 . 40. Corollary . Quantities , thus expressed by means of fractional exponents , may be used in all Division of Polynomials . calculations , and may be added 16 [ CH . I. & V. ALGEBRA .
... . a - 11b - 18-1a - 11b - 1 . Ans . 3 a - 1 . 40. Corollary . Quantities , thus expressed by means of fractional exponents , may be used in all Division of Polynomials . calculations , and may be added 16 [ CH . I. & V. ALGEBRA .
Page 17
... . Divide 14 a - 8bc3 d - 1e by 2 a b - 3 c5 d h . 1 Ans . 7a - 9b4c - 2d - 2eh - 1 . 14. Divide -3 am by 2 am + n b c - 1 . Ans . - a - b - 1 c . Division of Polynomials . 42. Problem . To divide one 2 * CH . I. § V. ] 17 DIVISION .
... . Divide 14 a - 8bc3 d - 1e by 2 a b - 3 c5 d h . 1 Ans . 7a - 9b4c - 2d - 2eh - 1 . 14. Divide -3 am by 2 am + n b c - 1 . Ans . - a - b - 1 c . Division of Polynomials . 42. Problem . To divide one 2 * CH . I. § V. ] 17 DIVISION .
Page 18
To which are Added Exponential Equations and Logarithms Benjamin Peirce. Division of Polynomials . 42. Problem . To divide one polynomial by an- other ... Division of Polynomials . 43. EXAMPLES . 1. Divide —16 18 [ CH . I. & V. ALGEBRA .
To which are Added Exponential Equations and Logarithms Benjamin Peirce. Division of Polynomials . 42. Problem . To divide one polynomial by an- other ... Division of Polynomials . 43. EXAMPLES . 1. Divide —16 18 [ CH . I. & V. ALGEBRA .
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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