Elements of AlgebraNew York, 1910 |
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a²b a²b² a³b ab² ab³ arithmetic arithmetic means average temperature ax² binomial Check coefficient consecutive numbers contains cross products cube denominator difference digits divided division divisor examples exceeds EXERCISE Find the numbers Find the side Find the sum Find the value following equations following expressions graph graphically Hence inches method miles per hour monomial multiplied negative number of dollars numbers is equal numerical value obtain polynomial prime factors problem proportional quadratic equation quotient radical ratio rectangle reduced remainder Resolve into prime Simplify simultaneous equations Solve the following square feet square root Substituting subtract surds Transposing triangle trinomial twice unknown number unknown quantities x²y x²y² x²y³ x³y x³y² xy² xy³ yards zero
Popular passages
Page 40 - ... the square of the second. In the second case, (ab)2 = a?-2ab + bi. (2) That is, the square of the difference of two numbers is equal to the square of the first, minus twice the product of the first by the second, plus the square of the second.
Page 81 - A trinomial belongs to this type, ie it is a perfect square, when two of its terms are perfect squares, and the remaining term is equal to twice the product of the square roots of these terms.
Page 118 - If the product of two numbers is equal to the product of two other numbers, either pair may be made the means, and the other pair the extremes, of a proportion.
Page 306 - Cloth, xii + 233 pages. 80 cents net. This Geometry introduces the student systematically to the solution of geometrical exercises. It provides a course which stimulates him to do original work and, at the same time, guides him in putting forth his efforts to the best advantage. The Schultze and Sevenoak Geometry is in use in a large number of the leading schools of the country. Attention is invited to the following important features : i. Preliminary Propositions are presented in a simple manner...
Page 183 - Or ж2 + 2x-24 = 0. 325. If both members of an equation are divided by an expression involving the unknown quantity, the resulting equation contains fewer roots than the original one. In order to obtain all roots of the original equation, such a common divisor must be made equal to zero, and the equation thus formed be solved. Eg let it be required to solve If we divide both members by x — 3, we obtain ж + 3 = 5 or x = 2.
Page 91 - If the numerator and denominator of each fraction is multiplied (or divided) by the same number, the value of the fraction will not change.
Page 163 - The number of terms is greater by 1 than the exponent of the binomial. 2. The exponent of a in the first term is the same as the exponent of the binomial, and decreases by 1 in each succeeding term.
Page 117 - A proportion is a statement expressing the equality of two ratios. | = foro:b = c:d are proportions. 178. The first and fourth terms of a proportion are the extremes, the second and third terms are the means. The last term is the fourth proportional to the first three. In the proportion a : Ь = с : d, a and d are the extremes, 6 and с the means.
Page 47 - To divide a polynomial by a monomial, divide each term of the dividend by the divisor and add the partial quotients.
Page 82 - According to § 65, ie i/te difference of the squares of two numbers is equal to the product of the sum and the difference of the two numbers.