HLRGAATPreISM_35799X_12_chR

HLRGAATPreISM_35799X_12_chR - Chapter R: Basic Algebraic...

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Chapter R: Basic Algebraic Concepts R.1: Exponents and P olynomials 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. is a polynomial. It is a monomial since it has one term. It has degree 11 since 11 is the highest exponent. 14. is a polynomial. It is a binomial since it has two terms. It has degree 12 since 12 is the highest exponent. 15. is a polynomial. It is a binomial since it has two terms. It has degree 6 since 6 is the sum of the exponents in the term (The term has degree 2.) 16. is a polynomial. It is a trinomial since it has three terms. It has degree 6 since 6 is the highest exponent. 17. is a polynomial. It is a binomial since it has two terms. It has degree 6 since 6 is the highest exponent. 18. is a polynomial. It is a binomial since it has two terms. It has degree 7 since 7 is the sum of the exponents in the term (The other term has degree 5.) 19. is a polynomial. It is a trinomial since it has three terms. It has degree 6 since 6 is the sum of the exponents in the term (The other terms have degree 4.) 20. is not a polynomial since positive exponents in the denominator are equivalent to negative exponents in the numerator. 21. is not a polynomial since the exponents are not integers. 22. 23. 1 4 m 3 2 3 m 2 1 5 2 1 1 ] 3 m 3 2 m 2 1 5 2 5 1 4 m 3 2 3 m 3 2 1 1 ] 3 m 2 2 m 2 2 1 1 5 1 5 2 5 m 3 2 4 m 2 1 10 1 3 x 2 2 4 x 1 5 2 1 1 ] 2 x 2 1 3 x 2 2 2 5 1 3 x 2 2 2 x 2 2 1 1 ] 4 x 1 3 x 2 1 1 5 2 2 2 5 x 2 2 x 1 3 ] 5 1 z 1 2 2 z 3 2 5 2 z 5 5] 5 z 1 > 2 1 2 z 3 > 2 2 5 z 5 > 2 5 p 1 2 p 2 1 5 p 3 ] 3 5 r 4 s 2 . 1 3 r 2 s 2 2 3 5 r 4 s 2 1 rs 3 ] 1 7 m 5 n 2 . ] 1 7 m 5 n 2 1 2 1 3 m 3 n 2 1 2 x 2 1 1 3 x 6 2 a 6 1 5 a 2 1 4 a 6 pq 18 p 5 q . 18 p 5 q 1 6 pq 9 y 12 1 y 2 ] 5 x 11 a r 8 s 2 b 3 5 r 8 ? 3 s 2 ? 3 5 r 24 s 6 ] a p 4 q b 2 5] a p 4 ? 2 q 2 b 5] p 8 q 2 1 ] 4 m 3 n 9 2 2 5 1 ] 4 2 2 1 m 3 2 2 1 n 9 2 2 5 4 2 m 6 n 18 or 16 m 6 n 18 1 2 x 5 y 4 2 3 5 2 3 1 x 5 2 3 1 y 4 2 3 5 2 3 x 15 y 12 or 8 x 15 y 12 1 6 4 2 3 5 6 4 ? 3 5 6 12 1 2 2 2 5 5 2 2 ? 5 5 2 10 1 ] 4 z 2 0 5 1, if z Þ 0 1 5 m 2 0 5 1, if m Þ 0 ] 2 0 5] 1 1 2 5] 1 2 0 5 1 1 ] 5 2 2 ? 1 ] 5 2 6 5 1 ] 5 2 2 1 6 5 1 ] 5 2 8 1 ] 4 2 3 ? 1 ] 4 2 2 5 1 ] 4 2 3 1 2 5 1 ] 4 2 5
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24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. To find the square of a binomial, find the sum of the square of the first term, twice the product of the two terms, and the square of the last term. 38. To find the product of the sum and difference of two terms, find the difference between the square of the first term and the square of the last term. 39. 40. 41. 42. 43. 44. 45. 46. 47. 9 q 2 1 30 q 1 25 2 p 2 31 3 q 1 5 2 2 p 431 3 q 1 5 2 1 p 4 5 1 3 q 1 5 2 2 2 1 p 2 2 5 31 3 q 2 2 1 2 1 3 q 21 5 2 1 1 5 2 2 4 2 p 2 5 16 y 2 2 8 y 1 1 1 8 yz 2 2 z 1 z 2 31 4 y 2 1 2 1 z 4 2 5 1 4 y 2 1 2 2 1 2 1 4 y 2 1 21 z 2 1 1 z 2 2 5 31 4 y 2 2 2 2 1 4 y 21 1 2 1 1 2 4 1 8 yz 2 2 z 1 z 2 5 4 p 2 2 12 p 1 9 1 4 pq 2 6 q 1 q 2 31 2 p 2 3 2 1 q 4 2 5 1 2 p 2 3 2 2 1 2 1 2 p 2 3 21 q 2 1 1 q 2 2 5 31 2
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This note was uploaded on 09/24/2011 for the course MATH 1310 taught by Professor Marks during the Spring '08 term at University of Houston.

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HLRGAATPreISM_35799X_12_chR - Chapter R: Basic Algebraic...

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