Algebra and Trigonometry by Harley Flanders and Justin J. Price (Auth.)

By Harley Flanders and Justin J. Price (Auth.)

Algebra and Trigonometry

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To multiply polynomials, treat them Uke any other sums: multiply each term of the first by each term of the second. Simplify the result by using the rule for exponents, then collecting all terms in the same power of x. 2 Compute: (a) SOLUTION (3JC + 2X5* - 1) (a) (b) (JC - 2)(4x2 + 5x + 6). Multiply each term of 3x + 2 by each term of 5* — 1 : (3x + 2)(5x - 1) = (3*)(5x) + (2)(5x) + ( 3 x ) ( - l ) + ( 2 ) ( - l ) = 15x2 + 10* - 3x - 2 = \5x2 + 7x - 2. (b) Same technique, only you get six terms instead of four: (JC - 2)(4JC 2 + 5JC + 6) = (JC)(4JC2) - (2)(4JC 2 ) + (*X5*) - (2)(5x) + (x)(6) - (2X6) = 4x3 - Sx2 + 5x2 - lOx + 6x - 12 = 4JC3 - Answer (a) 15x2 + Ix - 2 3x2 - Ax - 12.

15. 17. 19. 21. 2a(a2 + 4a + 1) = 2a3 + 8a2 + 1 a3 + b3 = (a + 6)3 0- 2 a- 2 = a 4 V*3 + 2x2 + x = x(x + 1) (25JC)(4JC) = lOOx X + Z Z 12. 14. 16. 18. 20. ^ V x + V> ' A: + y V3x + 5 + \/2x + 1 = V5x + 6 ^ 2 = a~2/3 (x/y2)2 = x/y4 x + x + x + x = x4 V*~ + λ/ϊχ = y/3x 22. x~2 = — 48 1. BASIC ALGEBRA 23. (x + \){y + l)(z + 1 ) = xyz + χ+γ + ζ+\ 24. l/y Λ: 27. 29. 31. 1+ 1 = x 1+ x (x + J>)3 = x 3 + 3Λ^ + γ3 xy 28. x + 8 , ,Γ „ =1+2 + 4 = 7 χ2 + 2χ + 2 - 2 4 = 2" 4 30. ^8 + 27 = 2 + 3 = 5 32. ( - 2 ) " 4 = - 2 ~ 4 .

Z 6 + 4z3 + 4 34. I602 + 80 + 1 35. x2y2 + 3x^ + 9 36. 9c2 - 30a/ + 25d2 37. (x2 + l) 2 + 2(x2 + 1) + 1 38. 9u2 + 9w + 1 39. a2b8 - 4ab4c2 + 4c4 40*. x2 + 2xy + y2 + 4xz + 4yz + 4z2. Explain these party games: 41. Take a number from 1 to 10. Square the number one larger and square the number one smaller. Subtract. Divide by the number you started with. Now you have 4. 42. Multiply your number by the number 4 larger. Add 4. Take the square root. Subtract the number you started with. Now you have 2.

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