Elements of Algebra: Including Sturms' Theorem |
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Page 36
... Divide 16x2 by 8x . Ans . 2x 2. Divide 15a2xy3 by 3ay . Ans . 5axy2 . 3. Divide 84ab3x by 1262 . Ans . 7abx . 4. Divide 96a4b2c3 by 12a2bc . Ans . Sa2bc2 . 5. Divide 144a9b8c7d5 by 36a4b6c6d . Ans . 4a5b2cd4 . 6. Divide 256a3bc2x3 by ...
... Divide 16x2 by 8x . Ans . 2x 2. Divide 15a2xy3 by 3ay . Ans . 5axy2 . 3. Divide 84ab3x by 1262 . Ans . 7abx . 4. Divide 96a4b2c3 by 12a2bc . Ans . Sa2bc2 . 5. Divide 144a9b8c7d5 by 36a4b6c6d . Ans . 4a5b2cd4 . 6. Divide 256a3bc2x3 by ...
Page 39
... divide the term a2 of the dividend by the term a of the divisor , the partial quotient is a , which we place under the divisor . We then multiply the divisor by a , and subtract the product a2 - ax from the dividend , and to the ...
... divide the term a2 of the dividend by the term a of the divisor , the partial quotient is a , which we place under the divisor . We then multiply the divisor by a , and subtract the product a2 - ax from the dividend , and to the ...
Page 41
... divide the first term on the left of the dividend by the first term on the left of the divisor , for the first term of the quotient ; muliply the divisor by this term and subtract the prod- uct from the dividend . II . Then divide the ...
... divide the first term on the left of the dividend by the first term on the left of the divisor , for the first term of the quotient ; muliply the divisor by this term and subtract the prod- uct from the dividend . II . Then divide the ...
Page 42
... Divide 95a 73a2 + 56a4 25 59a3 by 3a2 +5 11a 7a3 . 56a4 59a3 - 73a2 + 95a 25 | 743 1st rém . 35a3 + 15a2 + 55a 25 3a2 8a 11a + 5 5 2d remainder - 0 . GENERAL EXAMPLES . 1. Divide 10ab + 15ac by 54 42 [ CHAP . II . ELEMENTS OF ALGEBRA ...
... Divide 95a 73a2 + 56a4 25 59a3 by 3a2 +5 11a 7a3 . 56a4 59a3 - 73a2 + 95a 25 | 743 1st rém . 35a3 + 15a2 + 55a 25 3a2 8a 11a + 5 5 2d remainder - 0 . GENERAL EXAMPLES . 1. Divide 10ab + 15ac by 54 42 [ CHAP . II . ELEMENTS OF ALGEBRA ...
Page 43
... Divide 30ax 54x by 6x . 3. Divide 10x2y - 15y2 - 5y by 5y . 4. Divide 12а + Зах — 18ax2 by 3a . 5. Divide 6ax2 + 9a2x + a2x2 by ax . 6. Divide a2 + 2ax + x2 by a + x . 7. Divide a3 - 3a2y + 3ay2 - y3 by 8. Divide 24a2b 12a3cb2 6ab by ...
... Divide 30ax 54x by 6x . 3. Divide 10x2y - 15y2 - 5y by 5y . 4. Divide 12а + Зах — 18ax2 by 3a . 5. Divide 6ax2 + 9a2x + a2x2 by ax . 6. Divide a2 + 2ax + x2 by a + x . 7. Divide a3 - 3a2y + 3ay2 - y3 by 8. Divide 24a2b 12a3cb2 6ab by ...
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Common terms and phrases
affected algebraic quantities arithmetical arithmetical means arithmetical progression binomial co-efficient common difference consequently contain contrary signs cube root decimal deduced denominator denote derived polynomials divide dividend division entire number enunciation equa equation involving example expression extract the square factors figure find the square find the values formula fourth fraction given equation given number gives greater greatest common divisor hence inequality last term least common multiple letter logarithm monomial multiplicand multiplied negative nth root number of terms obtain operation ounces perfect square positive roots preceding problem progression proposed equation quan quotient Reduce remainder result rule satisfy second degree second member second term simplest form square root substituted subtract suppose take the equation third tion transformed transposing unity unknown quantity whence whole number ах
Popular passages
Page 32 - 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 277 - 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 29 - 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 181 - 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 182 - 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 92 - 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 348 - 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 36 - I. Divide the coefficient of the dividend by the coefficient of the divisor.
Page 110 - 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 204 - 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.
