By Charles Denlinger and Elaine Jacobson (Auth.)

ISBN-10: 0120595680

ISBN-13: 9780120595686

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**Sample text**

Which of the following are polynomials? polynomial. 7. 7x y - | 9. 1,597 11. 2 8. 2 2 4 Find the degree of each 8 + 9 x - 7x 10. 5 12. x 2 / 3 4 xy -llz 4 3 WORKING WITH POLYNOMIALS When adding or subtracting polynomials, we are merely "combining like terms". Two things should be remembered: (1) Only like terms can be combined. (2) To remove a pair of parentheses, each term inside the parentheses must be multiplied by the number outside the parentheses. EXAMPLE 1 (a) (4x+2) + (6x-3) = 4 x + 6 x + 2 - 3 = 10x-l (b) (2x + x - l ) - (x + 4 x - 5 ) = - x + 2 x - 4 x + x - l + 5 2 3 2 3 2 2 3 2 = -x - 2x + x + 4 (c) (3xy-4z) + (3x-xy + z) = 3xy - xy + 3x - 4 z + z = 2xy+ 3x- 3z (d) 2 x - 3 y - [4x- 2(x-y)] = 2x- 3y- [4x- 2x+2y] = 2x- 3y- [2x+ 2y] = -5y 32.

B) ax a - ; does NOT equal -—; . The x in the denomibx + cy b + cy n nator is not a factor of the whole denominator and it cannot be cancelled. 44. EXAMPLE 6 2 Canceling the x terms is an error of type (a) described above. (a) The correct way to simplify is Canceling the x s in this way is an error of type (b) described above. (b) The correct way to simplify is EXERCISE SET 1. 1 Which of the following are rational expressions? (a) (d) (b) (e) (c) (f) 489 In problems 2 - 1 9 , reduce each rational expression to lowest terms.

6x - x - 5x 18. 8x - 2x - 3x 19. 2x + 5x - 3 20. x - 13x + 36 21. 3 3 xy - x y 22. 6x - 7x - 3 23. 9x + 3 0 x + 25 24. x -81 25. x -2 2 2 2 2 J 4 2 2 2 X 2 + 3 X 2 2 2 Z 2 4 4 4 3 2 2 4 2 2 2 37. 4 THE BINOMIAL THEOREM The array of numbers 1 1 1 1 1 1 3 10 6 15 1 1 3 6 4 5 1 2 1 20 1 4 10 5 15 6 1 1 is known as Pascal's triangle. Observe that each inner entry is the sum of the two numbers above it. This pattern can be con tinued line-by-line without end. The binomial theorem asserts that the coefficients of the expanded form of (x + y ) n can be determined from Pascal's triangle, when n is a positive integer.

### Algebra Review by Charles Denlinger and Elaine Jacobson (Auth.)

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