Elements of Algebra: On the Basis of M. Bourdon, Embracing Sturm's and Horner's Theorems, and Practical ExamplesA. S. Barnes & Company, 1857 - 400 páginas |
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Página 41
... Ans . Ans . Tabx . -8a2bc2 . Ans . 4a5b2cd4 . - Ans . 16abcx . Ans . Ans . - 10abcx . - 16bcx4 . - 52. It follows from the preceding rule that the exact CHAP . II.J 41 DIVISION . Multiplication-Rule for Monomials and Signs 41-45.
... Ans . Ans . Tabx . -8a2bc2 . Ans . 4a5b2cd4 . - Ans . 16abcx . Ans . Ans . - 10abcx . - 16bcx4 . - 52. It follows from the preceding rule that the exact CHAP . II.J 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
... - · 3b2c2 by a2 — b2 . Ans . 3a2 — 562 + 3c2 . 6x4y ++ 6x3y2 + 15x3y3 — 9x2y 3x3 + 2x2y2 + 3y2 . - Ans . 2x3 - 3x2y2 + 5y ' . REMARKS ON THE DIVISION OF POLYNOMIALS . 58. The exact 18 [ CHAP . II ELEMENTS OF ALGEBRA .
... - · 3b2c2 by a2 — b2 . Ans . 3a2 — 562 + 3c2 . 6x4y ++ 6x3y2 + 15x3y3 — 9x2y 3x3 + 2x2y2 + 3y2 . - Ans . 2x3 - 3x2y2 + 5y ' . 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 , 12a35a2b + 7ab2 . 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 , 12a35a2b + 7ab2 . 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 common difference contrary signs cube root deduce denote the number derived polynomial Divide dividend entire number equal exactly divisible example exponent extract the square figures Find the factors find the values following RULE formula fractional unit given equation given number gives greater number greatest common divisor hence indicated inequality irreducible fraction last term leading letter least common multiple logarithm mixed quantity monomial multiplicand and multiplier nth power nth root number of terms obtain operation perfect square positive roots preceding problem proposed equation quotient radical sign real roots Reduce the polynomial remainder required to find result second degree second member second term simplest form square root substituted subtract suppose taken third transformed equation unknown quantity whence whole number X₁
Pasajes populares
Página 121 - Multiply the divisor, thus augmented, by the last figure of the root, and subtract the product from the dividend, and to the remainder bring down the next period for a new dividend.
Página 174 - For, we can find the value of one of the unknown quantities in terms of the other and known quantities...
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 39 - 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.
Página 10 - Logic is a portion of the art of thinking; language is evidently, and by the admission of all philosophers, one of the principal instruments or helps of thought; and any imperfection in the instrument or in the mode of employing it is confessedly liable, still more than in almost any other art, to confuse and impede the process and destroy all ground of confidence in the result.
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 contain 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 35 - We have, then, for the multiplication of polynomials, the following RULE. Multiply all the terms of the multiplicand by each term of the multiplier in succession, aff'ccting the product of any two terms with the sign plus, when tlieir signs are alike, and with the sign minus, when their signs
Página 41 - Divide the coefficient of the dividend by the coefficient of the divisor.
Página 200 - The cube of a number is equal to the cube of the tens, plus three times the product of the square of the tens by the units, plus three times the product of the tens by the square of the units, plus the cube of the units.