Elements of Algebra: On the Basis of M. Bourdon, Embracing Sturm's and Horner's Theorems : and Practical ExamplesA. S. Barnes & Burr, 1860 - 400 páginas |
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Página 41
... .x. Ant . - Sa2bc2 . Ans . - 4a5b2cd4 . Ans . 16abcx . Ans . 10abcx . Ans . - - 16bc.x + 52. It follows from the preceding rule that the exact CHAP . II . ] 41 DIVISION . Multiplication-Rule for Monomials and Signs 41-45.
... .x. Ant . - Sa2bc2 . Ans . - 4a5b2cd4 . Ans . 16abcx . Ans . 10abcx . Ans . - - 16bc.x + 52. It follows from the preceding rule that the exact CHAP . II . ] 41 DIVISION . Multiplication-Rule for Monomials and Signs 41-45.
Página 42
... exact division of monomials will be impossible : 1st . When the co - efficient of the dividend is not divisible by that of the divisor . 2d . When the exponent of the same letter is greater in the divisor than in the dividend . This ...
... exact division of monomials will be impossible : 1st . When the co - efficient of the dividend is not divisible by that of the divisor . 2d . When the exponent of the same letter is greater in the divisor than in the dividend . This ...
Página 46
... exact . In the second case the exact divi sion cannot be performed , and the quotient is expressed by writing the entire part obtained , and after it the remainder with its proper sign , divided by the divisor . SECOND EXAMPLE ...
... exact . In the second case the exact divi sion cannot be performed , and the quotient is expressed by writing the entire part obtained , and after it the remainder with its proper sign , divided by the divisor . SECOND EXAMPLE ...
Página 48
... 362c2 by a2 f2 . - Ans . 3a2 5b2 + 3c2 . - 6x1y1 + 6x3y2 + 15x3y3 - 9x2y + 10x2y5 + 15y5 by 3x3 + Qx2y2 + 3y2 . Ans . 2x3 - 3x2y2 + 5y3 REMARKS ON THE DIVISION OF POLYNOMIALS . 58. The exact 18 [ CHAP . II ELEMENTS OF ALGEBRA .
... 362c2 by a2 f2 . - Ans . 3a2 5b2 + 3c2 . - 6x1y1 + 6x3y2 + 15x3y3 - 9x2y + 10x2y5 + 15y5 by 3x3 + Qx2y2 + 3y2 . Ans . 2x3 - 3x2y2 + 5y3 REMARKS ON THE DIVISION OF POLYNOMIALS . 58. The exact 18 [ CHAP . II ELEMENTS OF ALGEBRA .
Página 49
... exact quotient , we may conclude that the exact division is im- possible . Take , for example , - 12a3 5a2b Tab2 - 1163 || 4a28ab + 3b2 . By considering only the letter a , the division would appear possible ; but regarding the letter b ...
... exact quotient , we may conclude that the exact division is im- possible . Take , for example , - 12a3 5a2b Tab2 - 1163 || 4a28ab + 3b2 . By considering only the letter a , the division would appear possible ; but regarding the letter b ...
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Términos y frases comunes
algebraic expression algebraic quantities approximating fraction arithmetical arithmetical progression becomes called co-efficient contrary signs cube root decimal places deduce denote the number derived polynomial Divide dividend entire number example exponent extract the square figures Find the factors Find the square find the values following RULE formula fourth fractional unit given equation given number gives greatest common divisor hence indicated inequality irreducible fraction last term leading letter least common multiple logarithm mixed quantity monomial multiplicand and multiplier negative roots nth power nth root number of terms obtain operation perfect square positive roots preceding problem proposed equation quotient radical sign real roots remainder required root required to find result second degree second member second term simplest form square root substituted subtract suppose supposition take the equation taken third unknown quantity whence whole number write
Pasajes populares
Página 174 - Find the value of one of the unknown quantities, in terms of the other and known quantities...
Página 290 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Página 286 - The logarithm of a number is the exponent of the power to which it is necessary to raise a fixed number, in order to produce the first number.
Página 117 - The first ten numbers are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 Roots.
Página 136 - Resolve the quantity under the radical sign into two factors, one of which is the greatest perfect power of the same degree as the radical.
Página 200 - RULE I. Separate the given number into periods. of three figures each, beginning at the right hand ; the left hand period will often con tain less than three places of figures.
Página 100 - 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 will it take each person to perform the same work alone.
Página 62 - Subtract the numerator of the subtrahend from the numerator of the minuend, and place the difference over the common denominator. EXAMPLES FOR PRACTICE.
Página 154 - B, departed from different places at the same time, and travelled towards each other. On meeting, it appeared that A had travelled 18 miles more than B ; and that A could have gone B's journey in 15| days, but B would have been 28 days in performing A's journey. How far did each travel ? Ans.
Página 222 - Consequently, teueя the index of the radical is divisible by the exponent of the power to which it is to be raised, perform the division, leaving the quantity under the radical sign unchanged.