Algebra for Colleges and SchoolsMacmillan, 1897 - 516 páginas |
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Página xii
... Remainder Theorem PAGE 258 264 · 264 265 266 • • 267 272 : 272 Symmetry · 273 • • XXXIII . Ratio XXXI . Indeterminate Equations of the First Degree . XXXII . Inequalities Miscellaneous Examples V. Proportion 276 • 279 283 . 286 291 ...
... Remainder Theorem PAGE 258 264 · 264 265 266 • • 267 272 : 272 Symmetry · 273 • • XXXIII . Ratio XXXI . Indeterminate Equations of the First Degree . XXXII . Inequalities Miscellaneous Examples V. Proportion 276 • 279 283 . 286 291 ...
Página 23
... remainder 5 a2 + 7 ab + 7 bc ? 14. From what expression must 3 ab + 5 bc - 6 ca be subtracted so as to leave a remainder 6 ca - 5 bc ? 15. To what expression must 7 x86 x2- 5x be added so as to make 9x36x7x2 ? - 16. To what expression ...
... remainder 5 a2 + 7 ab + 7 bc ? 14. From what expression must 3 ab + 5 bc - 6 ca be subtracted so as to leave a remainder 6 ca - 5 bc ? 15. To what expression must 7 x86 x2- 5x be added so as to make 9x36x7x2 ? - 16. To what expression ...
Página 43
... remainder is of lower dimensions [ Art . 29 ] than the divisor . EXAMPLES V. c . Divide 1. x8x29x12 by x2 + 3x + 3 . 2. 2 y3 - 3 y2 - 6 y 1 by 2 y2 — 5 y — 1 . - - 3. 6 m3 - m2 - 14 m + 3 by 3 m2 + 4 m −1 . 4. 6 a5 - 13 a1 + 4 a3 + 3 ...
... remainder is of lower dimensions [ Art . 29 ] than the divisor . EXAMPLES V. c . Divide 1. x8x29x12 by x2 + 3x + 3 . 2. 2 y3 - 3 y2 - 6 y 1 by 2 y2 — 5 y — 1 . - - 3. 6 m3 - m2 - 14 m + 3 by 3 m2 + 4 m −1 . 4. 6 a5 - 13 a1 + 4 a3 + 3 ...
Página 47
... remainder . - - EXPLANATION . The term ab2 in the divisor is missing , so we write 0 for the coefficient of this ... remainder is found by adding the rest of the columns and setting down the results without dividing by 2. By continuing ...
... remainder . - - EXPLANATION . The term ab2 in the divisor is missing , so we write 0 for the coefficient of this ... remainder is found by adding the rest of the columns and setting down the results without dividing by 2. By continuing ...
Página 56
... remainders are equal . 3. If equals are multiplied by equals , the products are equal . 4. If equals are divided by equals , the quotients are equal . 77. Consider the equation 7 x = 14 . It is required to find what numerical value x ...
... remainders are equal . 3. If equals are multiplied by equals , the products are equal . 4. If equals are divided by equals , the quotients are equal . 77. Consider the equation 7 x = 14 . It is required to find what numerical value x ...
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Términos y frases comunes
a²b a²b² a²x a²x² a³b ab² ab³ algebraic arithmetic means arithmetical ascending powers ax² ax³ b₁ binomial Binomial Theorem brackets bx² cents CHAPTER coefficient common difference compound expressions continued fraction convergent cube root denote digits dimes Divide division divisor equal EXAMPLES find the number Find the square Find the sum find the value following expressions greater harmonic means Hence highest common factor inequality letters logarithm lowest common multiple means miles an hour Multiply negative number of terms numerator and denominator obtain prove quadratic equation quotient ratio remainder Resolve into factors result rule rule of signs Simplify Solve square root subtraction surd symbols Theorem unknown quantity whence x²y x²y² x³y xy² xy³ yards zero
Pasajes populares
Página 167 - It is evident from the Rule of Signs that (1) no even power of any quantity can be negative; (2) any odd power of a quantity will have the same sign as the quantity itself. NOTE. It is especially worthy of notice that the square of every expression, whether positive or negative, is positive.
Página 262 - That is, if a quadratic equation be reduced to the form x?+px = q, the algebraic sum of the roots is equal to the coefficient of x with its sign changed, and the product of the roots is equal to the second member, with its sign changed.
Página 349 - The logarithm of a product is the sum of the logarithms of its factors.
Página 350 - The Integral Part of a logarithm is called the Characteristic, and the decimal part the Mantissa.
Página 183 - The sixth root of an expression is found by taking the cube root of the square root, or the square root of the cube root.
Página 102 - ... remainder. The lowest common multiple of two or more algebraic expressions is the expression of lowest degree which will contain them all without a remainder.
Página 287 - Four quantities are in proportion when the ratio of the first to the second is equal to the ratio of the third to the fourth.
Página 326 - A telegraph has 5 arms, and each arm has 4 distinct positions, including the position of rest: find the total number of signals that can be made.
Página 320 - From 7 Englishmen and 4 Americans a committee of 6 Is to be formed: in how many ways can this be done, (1) when the committee contains exactly 2 Americans, (2) at least 2 Americans...
Página 288 - Hence if any three terms of a proportion are given, the fourth may be found. Thus if a...