Elementary Algebra |
Other editions - View all
Common terms and phrases
a²b² ab² added algebraic expressions altitude arithmetic ax² binomial called Check coefficient common factor commutative law complete the square cube denominator difference digit in tens dimensions divided dividend division divisor EXERCISES Find exponent factor of x² feet Find the numbers Find the square Find the value following equations formula fraction gain given number Hence hypotenuse integers Johann Widmann length letters miles per hour minuend minus monomial multiply negative numbers number equals obtained Perform the following polynomial positive and negative positive numbers Principle XVIII quadratic equation quotient rational rectangle Reduce remainder represent result rods Rule satisfy sides signed numbers Simplify Solution Solve the equation Solve the following square root substituting symbols theorem twice unknown wide width write x²y xy² zero
Popular passages
Page 57 - 27. Hence division may be defined as the process of finding one of two factors when their product and the other factor are given. The given product is the dividend, the given factor is the divisor, and the factor to be found is the quotient. In dividing signed numbers the above
Page 363 - If the greater of two numbers is divided by the less, the quotient is 2 and the remainder is 1. If the less is increased by 20 and this result is divided by the greater increased by 3, the quotient is 2. Find the numbers. 10.
Page 186 - It is read the ratio of a to b equals the ratio of c to d, or briefly, a is to b as c is to d. Means and Extremes. The four numbers a, b, c, and d, when written
Page 215 - What are the numbers ? 4. The sum of two numbers is 8590 and their difference is 3480. What are the numbers ? 5. If the sum of two numbers is s and their difference is d, find the numbers. Solution. Let x represent one of the numbers and y the other. Then,
Page 30 - 66. (3) 31. Transposing Terms. By use of Principle VI, a term may be transposed from one member of an equation to the other, provided its sign is changed.
Page 114 - three times the square of the first term multiplied by the second, plus three times the first term multiplied by the square of the second, plus the cube of the second term. The above rule may be applied to find the cube of
Page 46 - -28 -400 The preceding exercises illustrate • • Principle VII 40. Rule. To add two numbers with like signs, find the sum of their absolute values, and prefix to this their common sign. To add two numbers with opposite signs, find the difference of their absolute values, and prefix to this the sign of that one whose absolute value is the greater. In case
Page 243 - 6) + c]c. This is now subtracted. Thus at each step a new term of the root is found by dividing the first term of the remainder by twice the first term of the root; and then a ne-w part of the power is built up and subtracted. Since the final remainder is zero, the square root is exact. Example 2. Find the square root of 16
Page 289 - The second root is not to be taken, for it is inadequate; people do not approve of negative roots." It was only after the time of Descartes (see page 240) that negative roots came into perfectly good standing. Imaginary Roots.* The imaginary roots of equations were entirely rejected by the Ancients. Cardan in Italy
Page 65 - a. A polynomial of two terms is called a binomial; one of three terms is called a trinomial. A term taken by itself is called a monomial. Terms which are to be added are called addends. Eg 5 a — 3 xy is a binomial; 5 a — 3 xy — f rt is a trinomial whose terms are the monomials 5 a,