Ray's Algebra Part Second: An Analytical Treatise, Designed for High Schools and Colleges |
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... Divide the .404-405 406-408 SYNTHETIC DIVISION ... 409 Transformation of Equations by Synthetic Division 410 Derived Polynomials - Law of .... 411-412 Transformation of Equations by Derived Polynomials 413 EQUAL ROOTS ... 414 LIMITS OF ...
... Divide the .404-405 406-408 SYNTHETIC DIVISION ... 409 Transformation of Equations by Synthetic Division 410 Derived Polynomials - Law of .... 411-412 Transformation of Equations by Derived Polynomials 413 EQUAL ROOTS ... 414 LIMITS OF ...
Page 34
... divide is called the divisor ; the quantity to be divided , the dividend ; the result of the operation , the quotient . ART . 68. In division , as in multiplication , there are four things to be considered , viz : The sign ; The ...
... divide is called the divisor ; the quantity to be divided , the dividend ; the result of the operation , the quotient . ART . 68. In division , as in multiplication , there are four things to be considered , viz : The sign ; The ...
Page 35
... DIVIDING ONE MONOMIAL BY ANOTHER.— Divide the coëfficient of the dividend by that of the divisor ; observing , that like signs give plus and unlike signs give minus . After the coefficient , write the letters common to both divisor and ...
... DIVIDING ONE MONOMIAL BY ANOTHER.— Divide the coëfficient of the dividend by that of the divisor ; observing , that like signs give plus and unlike signs give minus . After the coefficient , write the letters common to both divisor and ...
Page 36
... Divide 30a4b2 by 5a2b . 3. Divide -28x3y1z1 by —7xy2z . 4. Divide 35a2b3c by 5ab2 . 5. Divide 32xyz by -8xy . 6. Divide 42c3m2n by -3cmn . 7. Divide am + " and " - " each by x " . 8. Divide vmn by vm + r . - Ans . 2a3 and -2a3 . Ans ...
... Divide 30a4b2 by 5a2b . 3. Divide -28x3y1z1 by —7xy2z . 4. Divide 35a2b3c by 5ab2 . 5. Divide 32xyz by -8xy . 6. Divide 42c3m2n by -3cmn . 7. Divide am + " and " - " each by x " . 8. Divide vmn by vm + r . - Ans . 2a3 and -2a3 . Ans ...
Page 37
... Divide a2 + ab by a . 2. Divide 3xy + 2x2y by —xy . Ans . a + b Ans . -3-2x . Ans . Ans . 2a2-3z - 5 . 1-4x + 3a . 3. Divide 10a2z - 1522-25z by 5z . 4. Divide 3ab + 12abx - 9a2b by -3ab . 5. Divide 5x3y3 - 40a2x2y2 + 25a1xy by —5xy ...
... Divide a2 + ab by a . 2. Divide 3xy + 2x2y by —xy . Ans . a + b Ans . -3-2x . Ans . Ans . 2a2-3z - 5 . 1-4x + 3a . 3. Divide 10a2z - 1522-25z by 5z . 4. Divide 3ab + 12abx - 9a2b by -3ab . 5. Divide 5x3y3 - 40a2x2y2 + 25a1xy by —5xy ...
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Common terms and phrases
algebraic algebraic quantity arithmetical progression Binomial Theorem coëfficient continued fraction converging fraction cube root denominator denotes dividend divisible equa equal equation whose roots evident exactly divide EXAMPLES FOR PRACTICE exponent expressed extract the square Find the cube Find the greatest Find the number Find the square Find the sum find the value geometrical progression given number gives greater greatest common divisor Hence least common multiple less letters logarithm method minus monomial Multiply nth root nth term number of balls number of permutations number of terms operation perfect square polynomial positive root preceding proportion proposed equation quotient ratio real roots reduced remainder Required the numbers required to find result second degree second term square root Sturm's theorem substitute subtracted taken theorem third tion transformed transposing unknown quantity whence whole number zero
Popular passages
Page 83 - Any quantity may be transposed from one side of an equation to the other, if, at the same time, its sign, be changed.
Page 42 - 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 39 - Divide the first term of the dividend by the first term of the divisor, and write the result as the first term of the quotient. Multiply the whole divisor by the first term of the quotient, and subtract the product from the dividend.
Page 128 - 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.
Page 43 - The square of the difference of two quantities is equal to the square of the first, minus twice the product of the first by the second, plus the square of the second.
Page 35 - Obtain the exponent of each literal factor in the quotient by subtracting the exponent of each letter in the divisor from the exponent of the same letter in the dividend; Determine the sign of the result by the rule that like signs give plus, and unlike signs give minus.
Page 140 - ... and to the remainder bring down the next period for a dividend. 3. Place the double of the root already found, on the left hand of the dividend for a divisor. 4. Seek how often the divisor is contained...
Page 220 - What two numbers are those whose sum, multiplied by the greater, is equal to 77 ; and whose difference, multiplied by the lesser, is equal to 12 ? Ans.
Page 183 - Since the square of a binomial is equal to the square of the first term, plus twice the product of the first term by the second, plus the square of the second...
Page 28 - Multiply the coefficients of the two terms together, and to their product annex all the letters in both quantities, giving to each letter an exponent equal to the sum of its exponents in the two factors.