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. 1900 Excerpt: ...18. a: -4a? + 4. 19. 16a4-24a262 + 964. 20. 9 a;2 +18 a; + 9. 21. 2 a?-32 +128 a;. 22. 5 a3 + 20 a% + 20 a62. 23. (a;2-2a;)!! + 2(sc2-2a;)+l. 24. (x-y)2-2(a: -?/) + 1. 11. From Ch. V., Art. 6, we have jr2+ (a + 6)x + ab = (jr + a) (+). When a trinomial, arranged to descending powers of some letter, say x, can be ...
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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. 1900 Excerpt: ...18. a: -4a? + 4. 19. 16a4-24a262 + 964. 20. 9 a;2 +18 a; + 9. 21. 2 a?-32 +128 a;. 22. 5 a3 + 20 a% + 20 a62. 23. (a;2-2a;)!! + 2(sc2-2a;)+l. 24. (x-y)2-2(a: -?/) + 1. 11. From Ch. V., Art. 6, we have jr2+ (a + 6)x + ab = (jr + a) (+). When a trinomial, arranged to descending powers of some letter, say x, can be factored into two binomials, it must satisfy the following conditions: (i.) One term of the trinomial is the square of the letter of arrangement, i.e., of the common first term of the binomial factors. (ii.) The coefficient of the first power of the letter of arrangement in the trinomial is the algebraic sum of two numbers whose product is the remaining term of the trinomial. (iii.) These two numbers are the second terms of the binomial factors. 12. Ex. 1. Factor x2 + 8 x +15. The common first term of the binomial factors is evidently x. The second terms are two numbers whose product is 15, and whose sum is 8. By inspection we see that 3 + 5 = 8 and 3x5 = 15; that is, the second terms of the binomial factors are 3 and 5. Consequently, x2 + 8 x + 15 = (a; + 3) (a; + 5). Ex. 2. Factor x2-7 x +12. The common first term of the binomial factors is x. The second terms are two numbers whose product is 12, and whose sum is--7. Since their product is positive, they must be both positive or both negative; and since their sum is negative, they must be both negative. The possible pairs of negative factors of 12 are: --1 and-12;-2 and-6;-3 and-4. But since--3 + (--4) =--7, the second terms of the binomial factors are--3 and--4. Consequently x2--7 x +12 = (x--3) (x--4). Ex. 3. Factor aV + 5 ax--24. The common first term of the binomial factors is ax. The second terms are two numbers whose product is--24, and whose sum is 5. Since their product is negative, one must
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