# Elementary Algebra; First Course Volume 1

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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1915 edition. Excerpt: ...of the divisor and quotient, 18 a'-9 -3 + 27 a2 = 9 a2(2 a2-a + 3). That is, the factors of 18 a--9 a3 + 27 a2 are 9 a2 and 2 a2-a + 3. Hence the rule for finding the factors of a polynomial with a monomial factor: Find, by inspection, the monomial of highest power that will divide each term of the polynomial. Divide the polynomial by this monomial. The divisor and quotient are the monomial and polynomial factors, respectively, of the given polynomial. The division should always be performed mentally, and the work written as shown in the following example: Example.--Factor 2 nx2--4 ny2 + 6 nz2. 2 nx2-4 ny2 + 6 nz2 = 2 n(z2-2?/2 + 3 a2). 34. If, in two numbers of two digits each, the tens' digits are equal and the sum of the ones' digits is 10, the numbers may be expressed by 10t-f-u and 10t +10--u, respectively, in which t is the tens' digit, u the ones' digit of one, and 10--u the ones' digit of the other. Show that their product is 100I2 + 100t +10 u-u Show that this may be written 100 t(t +1) + -(10--ii). Hence, to multiply two numbers of which the tens' digits are equal, and the sum of the ones' digits is 10, take the product of the number of tens by a number one greater for the hundreds and annex the product of the ones. Thus, 74 x 76 = 5624; 69 x 61 = 4209; 43 x 47 = 2021. 35. Give at sight the products of the following: 23 x 27; 16 x 14; 26x24; 32 x38; 46x44; 56 x 54; 68x62; 77 x 73; 88 x 82; 93x97; 81x89; 84x86; 79x71; 75x75; 91x99; 94x96. 36. State a rule for squaring any number ending in 5 that follows as a special case of the rule in Exercise 34. 37. Give at sight the squares of the following: 25; 45; 35; 65; 85; 55; 95; 75; 105; 115. 85. Polynomials Factored by Grouping Terms.--Some polynomials that do not have monomial...show more

## Product details

• Paperback | 54 pages
• 189 x 246 x 3mm | 113g
• Miami Fl, United States
• English
• black & white illustrations
• 1236649141
• 9781236649140