A Complete Course in AlgebraLeach, Shewell, and Sanborn, 1885 |
From inside the book
Results 1-5 of 13
Page v
... 30 31 VI . DIVISION 36 Division of Monomials Division of Polynomials by Monomials . Division of Polynomials by Polynomials 37 38 39 VII . FORMULÆ . 44 VIII . FACTORING 51 IX . HIGHEST COMMON FACTOR FAGR 65 X. LOWEST COMMON.
... 30 31 VI . DIVISION 36 Division of Monomials Division of Polynomials by Monomials . Division of Polynomials by Polynomials 37 38 39 VII . FORMULÆ . 44 VIII . FACTORING 51 IX . HIGHEST COMMON FACTOR FAGR 65 X. LOWEST COMMON.
Page vi
Webster Wells. IX . HIGHEST COMMON FACTOR FAGR 65 X. LOWEST COMMON MULTIPLE . XI . FRACTIONS General Principles 75 To Reduce a Fraction to its Lowest Terms To Reduce a Fraction to an Entire or Mixed Quan- tity 888 80 80 82 To Reduce a ...
Webster Wells. IX . HIGHEST COMMON FACTOR FAGR 65 X. LOWEST COMMON MULTIPLE . XI . FRACTIONS General Principles 75 To Reduce a Fraction to its Lowest Terms To Reduce a Fraction to an Entire or Mixed Quan- tity 888 80 80 82 To Reduce a ...
Page 64
... b2 - c2 - d2 - 2ab - 2cd . 54. 1000 + 27 m® . 55. xxx + 1 . 58. ( x2 + 4 ) -16x2 . 59. x3 - y3 - 3xy ( x − y ) . - 56. 3 ( a2 — b2 ) — ( a — b ) 2 . 60. ( a2 + a - 4 ) 2 — 4 . IX . HIGHEST COMMON FACTOR . 121. A Common Factor 64 ALGEBRA .
... b2 - c2 - d2 - 2ab - 2cd . 54. 1000 + 27 m® . 55. xxx + 1 . 58. ( x2 + 4 ) -16x2 . 59. x3 - y3 - 3xy ( x − y ) . - 56. 3 ( a2 — b2 ) — ( a — b ) 2 . 60. ( a2 + a - 4 ) 2 — 4 . IX . HIGHEST COMMON FACTOR . 121. A Common Factor 64 ALGEBRA .
Page 65
Webster Wells. IX . HIGHEST COMMON FACTOR . 121. A Common Factor of two or more quantities is a quantity which will divide each of them without a remainder . Thus , 2xy ' is a common factor of 123y and 20x2y1 . 122. A prime quantity is ...
Webster Wells. IX . HIGHEST COMMON FACTOR . 121. A Common Factor of two or more quantities is a quantity which will divide each of them without a remainder . Thus , 2xy ' is a common factor of 123y and 20x2y1 . 122. A prime quantity is ...
Page 66
Webster Wells. RULE . To the highest common factor of the coefficients , annex the common letters , giving to each the lowest exponent with which it occurs in any of the given quantities . EXAMPLES . Find the highest common factors of ...
Webster Wells. RULE . To the highest common factor of the coefficients , annex the common letters , giving to each the lowest exponent with which it occurs in any of the given quantities . EXAMPLES . Find the highest common factors of ...
Other editions - View all
Common terms and phrases
a²+2ab+b² a²b² a³b ab+b² ab² ab³ Adding Algebra arithmetical means arithmetical progression ax² ax³ binomial cents change the sign coefficient cologarithm Completing the square cube root decimal derive the formulæ digits dividend divisor EXAMPLES exponent expression Extracting the square Find the H.C.F. Find the value Find two numbers following equations following rule formula fraction geometrical progression Hence highest common factor last term less logarithm lowest common multiple mantissa monomial Multiplying Note number of terms parenthesis perfect square polynomial positive proportion QUADRATIC EQUATIONS quotient radical sign Reduce the following remainder Required the number result rods rule of Art second term simplest form Solve the equation Solve the following square root subtract third Transposing trial-divisor twice unknown quantity Whence
Popular passages
Page 166 - Arts. 200 and 201 we derive the following rule : Extract the required root of the numerical coefficient, and divide the exponent of each letter by the index of the root.
Page 213 - In any trinomial square (Art. 108), the middle term is twice the product of the square roots of the first and third terms...
Page 44 - ... the product of the two, plus the square of the second. In the third case, we have (a + b) (a — 6) = a2 — b2. (3) That is, the product of the sum and difference of two quantities is equal to the difference of their squares.
Page 49 - The exponent of b in the second term is 1, and increases by 1 in each succeeding term.
Page 255 - The first and fourth terms of a proportion are called the extremes; and the second and third terms the means. Thus, in the proportion a : b = с : d, a and d are the extremes, and b and с the means.
Page 258 - In a series of equal ratios, any antecedent is to its consequent, as the sum of all the antecedents is to the sum of all the consequents. Let a: b = c: d = e:f.
Page 5 - If equal quantities be divided by the same quantity, or equal quantities, the quotients will be equal. 5. If the same quantity be both added to and subtracted from another, the value of the latter will not be changed.
Page 44 - 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 107 - Any term may be transposed from one side of an equation to the other by changing its sign. For, consider the equation x + a = b.
Page 227 - A' courier proceeds from P to Q in 14 hours. A second courier starts at the same time from a place 10 miles behind P, and arrives at Q at the same time as the first courier. The second courier finds that he takes half an hour less than the first to accomplish 20 miles. Find the distance from P to Q.