Elements of Algebra: Including Sturms' Theorem |
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Page 5
... Monomials 40-42 Rule for Polynomials and Signs 42-45 Remarks - Theorems Proved .... 45-48 Of Factoring Polynomials . 48-49 Division of Monomials - Rule . 49-52 Signification of the Symbol ao ..... 52-54 Division of Polynomials - Rule ...
... Monomials 40-42 Rule for Polynomials and Signs 42-45 Remarks - Theorems Proved .... 45-48 Of Factoring Polynomials . 48-49 Division of Monomials - Rule . 49-52 Signification of the Symbol ao ..... 52-54 Division of Polynomials - Rule ...
Page 6
... Monomials . Of Polynomials ..... Calculus of Radicals of the Second Degree Addition and Subtraction - Of Radicals .. Multiplication , Division , and Transformation . CHAPTER VI . EQUATIONS OF THE SECOND DEGREE . Equations of the Second ...
... Monomials . Of Polynomials ..... Calculus of Radicals of the Second Degree Addition and Subtraction - Of Radicals .. Multiplication , Division , and Transformation . CHAPTER VI . EQUATIONS OF THE SECOND DEGREE . Equations of the Second ...
Page 8
... Monomials Of Polynomials . 221-224 Calculus of Radicals - Transformation of Radicals 224-227 Addition and Subtraction of Radicals . 227 Multiplication and Division 228 Formation of Powers and Extraction of Roots .... 229 Different Roots ...
... Monomials Of Polynomials . 221-224 Calculus of Radicals - Transformation of Radicals 224-227 Addition and Subtraction of Radicals . 227 Multiplication and Division 228 Formation of Powers and Extraction of Roots .... 229 Different Roots ...
Page 15
... monomial , or simply , a term . Thus , 3a , 5a2 , 7a3b2 , are monomials , or single terms . 20. An algebraic expression composed of two or more terms , separated by the sign + or - , is called a polynomial . For example , 3a - 56 , and ...
... monomial , or simply , a term . Thus , 3a , 5a2 , 7a3b2 , are monomials , or single terms . 20. An algebraic expression composed of two or more terms , separated by the sign + or - , is called a polynomial . For example , 3a - 56 , and ...
Page 21
... monomials , The result of the addition is За 56 2c 3a +56 + 2c an expression which cannot be reduced to a more simple form . Again , add together the monomials { 4a263 2a2b3 7a263 The result , after reducing ( Art . 29 ) , is 13a2b3 Let ...
... monomials , The result of the addition is За 56 2c 3a +56 + 2c an expression which cannot be reduced to a more simple form . Again , add together the monomials { 4a263 2a2b3 7a263 The result , after reducing ( Art . 29 ) , is 13a2b3 Let ...
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Common terms and phrases
affected algebraic quantities arithmetical means arithmetical progression binomial called co-efficient common difference consequently contain contrary signs cube root Cx² decimal deduced denominator denote divide dividend division entire number enunciation equa equal equation involving example exponent expression extract the square factors figure find the values formula fourth fraction given equation given number gives greater greatest common divisor hence inequality last term least common multiple less logarithm monomial multiplicand multiplied negative nth root number of terms obtain operation ounces perfect square permutations problem proportion proposed equation quan quotient radical sign Reduce remainder result rule satisfy second degree second member second term simplest form square root substituted subtract suppose supposition take the equation third tion tities total number transposing unity unknown quantity whence whole number ах
Popular passages
Page 30 - That is, the square of the sum of two quantities is equal to the square of the first, plus twice the product of the first by the second, plus the square of the second.
Page 275 - The characteristic of a number less than 1 is found by subtracting from 9 the number of ciphers between the decimal point and the first significant digit, and writing — 10 after the result.
Page 27 - Hence, for the multiplication of polynomials we have the following RULE. Multiply all the terms of the multiplicand by each term of the multiplier, observing that like signs give plus in the product, and unlike signs minus.
Page 179 - To express that the ratio of A to B is equal to the ratio of C to D, we write the quantities thus : A : B : : C : D; and read, A is to B as C to D.
Page 180 - If the product of two quantities is equal to the product of two other quantities, two of them may be made the extremes, and the other two the means of a proportion.
Page 90 - If A and B together can perform a piece of work in 8 days, A and C together in 9 days, and B and C in 10 days : how many days would it take each person to perform the same work alone ? Ans.
Page 346 - VARIATIONS of signs, nor the number of negative roots greater than the number of PERMANENCES. Consequence. 328. When the roots of an equation are all real, the number of positive roots is equal to the number of variations, and the number of negative roots to , the number of permanences.
Page 34 - I. Divide the coefficient of the dividend by the coefficient of the divisor.
Page 108 - Which proves that the square of a number composed of tens and units, contains the square of the tens plus twice the product of the tens by the units, plus the square of the units.
Page 202 - In each succeeding term the coefficient is found by multiplying the coefficient of the preceding term by the exponent of a in that term, and dividing by the number of the preceding term.