By Harley Flanders; Justin J Price
ISBN-10: 0122596668
ISBN-13: 9780122596667
ISBN-10: 1483265080
ISBN-13: 9781483265087
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Extra resources for Algebra
Example text
Yab2c5 14. { A 7. V50 j 18x3 1 1. 3. (y + z)4 15. Iii4 4. /;5 V'ill 12. V6 V3 8. 16. \/27 . 64 . 125 28 1. BASIC ALGEBRA 17. 21. h6 {/8a3b9 18. V8T 19. \132 20. 22. {II0,000u2 23. y64u5v6 24. Find an equivalent expression without radicals in the denominator: l Vx + Vy V2 25. v'6 26. 28. 27. v'6 + V2 Vx - vY Compute and simplify: 29. 30. ( Vx + 3 yy)2 32. 33. /2 ) ( Vx Jxr _ vx Vx6 36. v'3 1 ( 34. VxY v'3 ) + + x2 39. ya2 41. v'3 + 2 = ajl + (�)2 40. v'3 1 v'3 - l -3 2 Prove for n-th roots: 44. rule (2) 43.
The degree of a polynomial is the highest exponent occurring with non-zero coefficient. Standard notation is The zero polynomial/(x) = 0 is not assigned a degree. The coefficient an is called the leading coefficient, and the term an x n is called the leading term. Polynomials have special names according to degree: Constant polynomial (zero degree): f(x) = a0 • Linear polynomial (first degree): f(x) a0 + a1x, Quadratic polynomial (second degree): f(x) = a0 + a1 x + a2 x2, a2 f. 0. Cubic polynomial (third degree): f(x) = a0 + a1x + a2x2 + a3x3, a3 f.
And x +y x-l It is not immediately clear that their sum is again a rational expression, a single quotient of polynomials. However, guided by our experience with rational numbers, we express the summands as quotients with a common denominator, and then add the numerators. 2 Compute: (a) x y + 3x - y 3x + y (b) 2x + I 2 l + . X2 - 4 X + 2 X - 2 --- -- -- (a) A common denominator is (3x - y)(3x + y): x y x(3x + y) (3x - y)y + = -3x-+ - y 3x + y (3x - y)(3x + y) (3x - y)(3x + y) _ x(3x + y) + (3x - y)y _ 3x2 + 4xy - yz - (3x - y)(3x + y) 9xZ - y z SOLUTION ------ (b) A common denominator is x2 - 4 = (x + 2)(x -2): 2x + l 2 l 2x + I 2(x - 2) --x+2 = + + x2 - 4 x + 2 x - 2 x2 - 4 x2 - 4 x2 - 4 (2x + 1 ) + 2(x - 2) - (x + 2) 3x - 5 = - x2 - 4 .
Algebra by Harley Flanders; Justin J Price
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