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. 1912 Excerpt: ...a2--4 54. a3 ] 9a2x + 6ax2 48. a2-4a + 4 55. a3 + 6a2x + 9ax2 49. a3--4a 56. a5--ax4 50. a--4a2 + 4a 57. a5 + ax 51. a4-4a3 + 4a2 58. (a + x)2-9 52. x3-6x 59. (a + b)2-(x-y-a)2 60. Make up and work an example in factoring in each of the cases treated thus far. 61. How many of the examples in this Exercise can you work ...
Read More
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. 1912 Excerpt: ...a2--4 54. a3 ] 9a2x + 6ax2 48. a2-4a + 4 55. a3 + 6a2x + 9ax2 49. a3--4a 56. a5--ax4 50. a--4a2 + 4a 57. a5 + ax 51. a4-4a3 + 4a2 58. (a + x)2-9 52. x3-6x 59. (a + b)2-(x-y-a)2 60. Make up and work an example in factoring in each of the cases treated thus far. 61. How many of the examples in this Exercise can you work at sight? 62. How many of the examples in Exercise 2 (p. 13) can you now work at sight? Case IV 94. A Trinominal of the Form x2 + bx + c. It was found in Art. 79 (p. 117) that on multiplying two binomials like x + 3 and x--5, the product, x2--2x--15, was formed by taking the algebraic sum of + 3 and--5 for the coefficient of x (viz.--2), and taking their product (--15) for the last term of the result. Hence, in undoing this work to find the factors of x2--2x--15, the essential part of the process is to find two numbers which, added together, will give--2 and, multiplied together, will give--15. Ex. 1. Factor x2 + x + 30. The pairs of numbers whose product is 30 are 30 and 1, 15 and 2, 10 and 3, 6 and 5. Of these, that pair whose sum is 11 is 6 and 5. Hence, x2 + 1Ix + 30 = (x + 6) (x + 5) Factors Ex. 2. Factor x2-x-30. It is necessary to find two numbers whose product is--30, and whose sum is--1. Since the sign of the last term is minus, the two numbers must be one positive and the other negative; and since their sum is--1 the greater number must be negative. x1-x-30 = (x-6) (x + 5) Factors Ex. 3. Factor x2 + 3xy-0y2. Since 5y and--2y, added give 3y, and multiplied give--Wy1, x2 + 3xy-1Oy2 = (x + %) (x-2y) Factors Hence, in general, to factor a trinomial of the form x2 + bx + c, Find two numbers which, multiplied together, produce the third term of the trinomial and, added together, give the coefficient of the second term; x (or whatever takes...
Read Less
Add this copy of Durell's Introductory Algebra to cart. $59.74, good condition, Sold by Bonita rated 4.0 out of 5 stars, ships from Newport Coast, CA, UNITED STATES, published 2016 by Palala Press.