# Algebra for college students by Bernard Kolman; Arnold Shapiro

By Bernard Kolman; Arnold Shapiro

Similar elementary books

Rank-Deficient and Discrete Ill-Posed Problems: Numerical Aspects of Linear Inversion

Here's an outline of recent computational stabilization tools for linear inversion, with functions to a number of difficulties in audio processing, scientific imaging, seismology, astronomy, and different parts. Rank-deficient difficulties contain matrices which are precisely or approximately rank poor. Such difficulties usually come up in reference to noise suppression and different difficulties the place the aim is to suppress undesirable disturbances of given measurements.

Calculus: An Applied Approach

Designed in particular for enterprise, economics, or life/social sciences majors, Calculus: An utilized strategy, 8/e, motivates scholars whereas fostering realizing and mastery. The e-book emphasizes built-in and fascinating functions that convey scholars the real-world relevance of themes and ideas.

Algebra, Logic and Combinatorics

This e-book leads readers from a easy beginning to a complicated point knowing of algebra, good judgment and combinatorics. excellent for graduate or PhD mathematical-science scholars searching for assist in figuring out the basics of the subject, it additionally explores extra particular components equivalent to invariant conception of finite teams, version idea, and enumerative combinatorics.

Extra info for Algebra for college students

Sample text

2 when x = 4. 1. EJ � 54. 25. = 55. Write a polynomial giving the area of a circle of radius r. 56. Write a polynomial giving the area of a triangle of base b and height h. S 57. 3. What does each of the following polynomials represent? 3 T 1 58. E. T. stock at \$60 per share. What does the polynomial 55x + 45y + 60z represent? 2 ADDITION AND SUBTRACTION OF POLYNaVUALS Those terms of a polynomial which differ only in their coefficients are called like terms. Here are some examples of like terms: 4x 2 and -5xy3 and 2x 2y 2 and - 3x 2 17xy3 -2x 2y 2 We add polynomials by adding the coefficients of like terms.

3. 5. 7. 9. 1 1. 13. 15. 17. 19. 2+5=5+2 -2 · 5 = 5(-2) (4 + 3)2 = 4 . 2 + 3 . 2 -2(4 - 5) ( -2)(4) - 2( -5) -3 + (2 + 5) = ( - 3 + 2) + 5 3 +a=a+3 2(ab) (2a)b 2(xy) = x(2y) 5 + (a + 2) = 2 + (5 + a) = = (3 . 2)( -4) = 3[(2)( -4)] 2(4 + 5) = 2 . 4 + 2 . 5 3(2 - 4) = 3 . 2 - 3 . 4 (3 + 2) + 4 3 + (2 + 4) (2 -5) + 8 2 + ( -5 + 8) 2(x + 2) = 2x + 4 5(a + b) = 5(b + a) 4(a + b) 4b + 4a (5x)y = 5(yx) = = = Give examples showing that the operation of subtraction does not satisfy the commutative and associative laws.

2 Add the given polynomials in each of the following. _ l; l l. Find the mistake(s) in each of the following. Obtain the correct answer. = l = = Subtract the second polynomial from the first. l l. Subtract the first polynomial from the second. = 23. 25. 27. 29. 31. 33. 35. a2bc 3xy2z -4x2 ab2c 2ab3 -3a2bc -4ab3 3 \$60 36. \$50 \$55x y \$20 37. \$260 x \$13 z \$17 x y 38. S + + + + + + + + + +s Simplify by combining like terms. T. stock at per share and y shares of Exxon stock at per share. E. stock at per share and shares of Bethlehem Steel stock at per share.