Remainder Theorem Factor Theorem Case VII: To Factor Polynomials which have a Binomial Factor Case VIII: To Factor a Polynomial of Four Terms Solution of Equations — Imaginary Numbers 93 94 96 98 99 Least Common Multiple of Quantities readily Factored and those not Formulae for the Solution of an Equation of the First Degree in One Unknown Quantity 158 CHAPTER II PROBLEMS WHICH LEAD TO EQUATIONS OF THE FIRST DEGREE Problems Solved for Illustration CHAPTER III LITERAL EQUATIONS IN ONE UNKNOWN NUMBER Numerical and Literal Equations Exercise for Illustration CHAPTER IV PROBLEMS INVOLVING LITERAL EQUATIONS Formulae and Rules Problems Solved for Illustration CHAPTER V INTERPRETATION OF THE SOLUTION OF PROBLEMS Positive and Negative Solutions Zero Solutions Indeterminate Solutions Infinite Solutions CHAPTER VI SIMULTANEOUS LINEAR EQUATIONS IN TWO UNKNOWN QUANTITIES Indeterminate Equations Independent Equations Incompatible Equations Equivalent Systems of Equations. The Solution of two Equations of the First Degree — Elimination by Two Equations of the First Degree which have a Common Root 164 175 176 180 182 187 190 192 193 198 199 200 201 204 207 212 218 230 231 232 233 236 237 CHAPTER VIII GENERAL SOLUTION OF A SYSTEM OF THREE EQUATIONS Examples of Three Equations of the First Degree Given One Solution of ax-by=c in Positive Integers, to Find the General Solution General Solution of Two Equations BOOK III INVOLUTION-EVOLUTION Index Law of Involution. 238 242 251 256 259 262 264 265 268 270 272 274 FRACTIONAL AND NEGATIVE EXPONENTS CHAPTER I INVOLUTION Powers of Monomials, Fractions, Binomials, and Polynomials 277 278 283 284 286 287 290 295 299 303 Theorems: I, a×a"=am+"; II, a”÷a”=am¬"; III; IV; V; etc. 309 312 V; etc.. 313 321 CHAPTER IV RELATIVE MAGNITUDE OF POSITIVE AND NEGATIVE QUANTITIES 323 324 Conventions concerning Relative Magnitudes 331 334 CHAPTER V Addition, Subtraction, Multiplication, and Division of Irrationals 345 Pure Imaginary Numbers and their Properties Addition, Multiplication, Division by i and Powers of i 373 374 Addition, Subtraction, Multiplication, and Division of Pure Imaginaries 376 Complex Numbers 379 Solution of the Equation + px+q=0 and Condition for Real, Equal, and Imaginary Roots 401 CHAPTER IV FACTORING OF A TRINOMIAL Factors of x+px + q 404 405 Factors of a+bx+c and ax2+ 2 bxy + cy2+2 dx + 2 CHAPTER V PROBLEMS IN EQUATIONS OF THE Second Degree in One UNKNOWN QUANTITY RELATIONS BETWEEN the CoefficienTS AND ROOTS OF A QUADRATIC EQUATION An Equation of the Second Degree has but Two Roots Properties of the Roots CHAPTER VII EQUATIONS WHICH ARE REDUCIBLE TO THE SECOND DEGREE 422 423 424 The Biquadratic Equation ar1+b2+c=0 427 Irrational Equations 428 Solution of ax+2bx+21 √ ax2+2bx+c=p and ax2 + bxn+c= 430 Reciprocal Equations 431 |