Solutions to Try Its

1. The degree is 6, the leading term is [latex]-{x}^{6}[/latex], and the leading coefficient is [latex]-1[/latex].

2. [latex]2{x}^{3}+7{x}^{2}-4x - 3[/latex]

3. [latex]-11{x}^{3}-{x}^{2}+7x - 9[/latex]

4. [latex]3{x}^{4}-10{x}^{3}-8{x}^{2}+21x+14[/latex]

5. [latex]3{x}^{2}+16x - 35[/latex]

6. [latex]16{x}^{2}-8x+1[/latex]

7. [latex]4{x}^{2}-49[/latex]

8. [latex]6{x}^{2}+21xy - 29x - 7y+9[/latex]

Solutions to Odd-Numbered Exercises

1. The statement is true. In standard form, the polynomial with the highest value exponent is placed first and is the leading term. The degree of a polynomial is the value of the highest exponent, which in standard form is also the exponent of the leading term.

3. Use the distributive property, multiply, combine like terms, and simplify.

5. 2

7. 8

9. 2

11. [latex]4{x}^{2}+3x+19[/latex]

13. [latex]3{w}^{2}+30w+21[/latex]

15. [latex]11{b}^{4}-9{b}^{3}+12{b}^{2}-7b+8[/latex]

17. [latex]24{x}^{2}-4x - 8[/latex]

19. [latex]24{b}^{4}-48{b}^{2}+24[/latex]

21. [latex]99{v}^{2}-202v+99[/latex]

23. [latex]8{n}^{3}-4{n}^{2}+72n - 36[/latex]

25. [latex]9{y}^{2}-42y+49[/latex]

27. [latex]16{p}^{2}+72p+81[/latex]

29. [latex]9{y}^{2}-36y+36[/latex]

31. [latex]16{c}^{2}-1[/latex]

33. [latex]225{n}^{2}-36[/latex]

35. [latex]-16{m}^{2}+16[/latex]

37. [latex]121{q}^{2}-100[/latex]

39. [latex]16{t}^{4}+4{t}^{3}-32{t}^{2}-t+7[/latex]

41. [latex]{y}^{3}-6{y}^{2}-y+18[/latex]

43. [latex]3{p}^{3}-{p}^{2}-12p+10[/latex]

45. [latex]{a}^{2}-{b}^{2}[/latex]

47. [latex]16{t}^{2}-40tu+25{u}^{2}[/latex]

49. [latex]4{t}^{2}+{x}^{2}+4t - 5tx-x[/latex]

51. [latex]24{r}^{2}+22rd - 7{d}^{2}[/latex]

53. [latex]32{x}^{2}-4x - 3[/latex] m²

55. [latex]32{t}^{3}-100{t}^{2}+40t+38[/latex]

57. [latex]{a}^{4}+4{a}^{3}c - 16a{c}^{3}-16{c}^{4}[/latex]