# Complete Algebra

Allyn and Bacon, 1917 - Algebra - 624 pages
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### Contents

 ADDITION AND SUBTRACTION OF ALGEBRAIC EXPRESSIONS ix Associative and Commutative Laws of Addition xi MULTIPLICATION AND DIVISION OF ALGEBRAIC EXPRES V 84 SIONS 87 Exponents 101 490 92 SPECIAL PRODUCTS AND QUOTIENTS 108 FACTORS OF ALGEBRAIC EXPRESSIONS 122 EQUATIONS SOLVED BY FACTORING 147 The Pythagorean Theorem 151 COMMON FACTORS AND MULTIPLES 155 ALGEBRAIC FRACTIONS IX X 160 Fractional Notation 161 EQUATIONS INVOLVING FRACTIONS 181 RATIO AND PROPORTION XII 187 LITERAL EQUATIONS AND THEIR USES 196 Literal Equations Formulas 206 XIV 207 GRAPHIC REPRESENTATION 230 Graphic Representation of Equations 239 SQUARE ROOTS AND RADICALS 239 FURTHER OPERATIONS ON RADICALS 262 XVIII 263 Quadratic Equations Imaginary Roots 284 XIX 297 SIMULTANEOUS EQUATIONS OF THE FIRST DEGREE QUADRATIC EQUATIONS SYSTEMS OF QUADRATICS 302 THE BINOMIAL FORMULA 308 The Binomial Formula 311 VARIABLES AND FUNCTIONS 312 REVIEW EXERCISES 318 INTERMEDIATE ALGEBRA 352 DEFINITIONS AND FUNDAMENTAL LAWS 353 FUNDAMENTAL OPERATIONS 361 FACTORING 379
 SYSTEMS OF EQUATIONS SOLVED BY DETERMINANTS 434 122 436 GRAPHIC REPRESENTATION OF EQUATIONS 446 Determinants 452 147 458 155 465 160 468 181 487 188 494 196 499 207 507 Number System 510 230 522 240 534 602616 X XI POWERS AND ROOTS XII XIII THE NUMBER SYSTEM OF ALGEBRA XIV QUADRATIC EQUATIONS XV SYSTEMS OF QUA... 544 GRAPHIC REPRESENTATION OF QUADRATICS 558 262 567 PROGRESSIONS XVII 572 278 584 BINOMIAL FORMULA 587 LOGARITHMS 593 Logarithms 601 COLLEGE ENTRANCE EXAMINATIONS RATIO VARIATION and Proportion NUMBER EXPONENTS AND RADICALS 602 Division of the Sum or Difference of Two Numbers IV V Division of the Product of Several Factors VI Deducing One Equation from Another VII A... 605 15 606 18 607 47 611 51 613 59 393 242 Copyright

### Popular passages

Page 471 - Divide the first term of the remainder by three times the square of the first term of the root, and write the result as the next term of the root.
Page 380 - R is not zero, and the division is not exact. That is, x — a is not a factor of D. Hence : If a polynomial in x reduces to zero when a particular number a is substituted for x, then x — a is a factor of the polynomial, and if the substitution of a for x does not reduce the polynomial to zero, then x — a is not a factor.
Page 188 - In a series of equal ratios, the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent.
Page 242 - ... the given expression. Divide the first term of the remainder by twice the first term of the root, and add the quotient to the part of the root already found, and also to the trial-divisor.
Page 108 - 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 591 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Page 451 - The number of vibrations per second of a pendulum varies inversely as the square root of the length. If a pendulum 39.1 inches long vibrates once in each second, how long is a pendulum which vibrates 3 times in each second ? 13.
Page 329 - В working together can do a piece of work in 6 days. A can do it alone in 5 days less than B. How long will it require each when working alone ? 15.
Page 31 - Any term may be transposed from one member of an equation to the other, provided its sign be changed.
Page 149 - The formula states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the base and altitude.