Algebra 1 Common Core Student Edition, Grade 8-9

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7z2 + 23z + 6

z 2 + 2 z — 3

3z2 + 12z

Simplify e a ch expression. State an y ex clu d ed values.

31.r 2 + 1 0 r + 2 5^2 r 9r — 5 32. 33.

5t2 + 6 t~ 8

3t2 + 5 t - 2

34.

37.

32a

16a2 - 8a

4a2 - 8a - 5

15 - a - 2 a 2

35.

38. 16 + 16m + 3mm 2 _3m — 28

36.

39.

2s2 + s

10c + c2 - 3c3

5c2 - 6c - 8

40. Think About a Plan In th e figure at th e right, w h at is the
    ratio of the area of th e sh ad e d triangle to th e area of the
    rectangle? Write your answ er in sim plified form.
    
    
    • W hat is an expression for th e length of th e rectangle?
    
    
    • How do you find th e area of a triangle?
    
    
    
    


41. Writing Is ^ T T t^ie sam e as x - 3? Explain.
    ^2 5 1 42. a. Construction To keep h eating costs dow n for a building, architects w an t th e
    ratio of surface area to volum e to be as sm all as possible. W hat is an expression
    for the ratio of surface area to volum e for each figure?
    i. square prism ^7 ii. cylinder

j—

b. For each figure, w h at is th e ratio of surface area to volum e w h en

b = 12 ft, h = 18 ft, an d r = 6 ft?

43. Error Analysis A stu d en t sim plified a rational expression as
    show n at th e right. D escribe an d correct th e error.


44. Banking A b an k account w ith principal P earns interest at rate
    r (expressed as a decim al), co m p o u n d ed annually. W hat is the
    ratio of th e balance after 3 yr to th e balance after 1 yr? Write r
    as a decim al.


45. Open-Ended W rite a rational expression th a t has 4 a n d —3 as excluded values.

Write a ratio in simplified form of the area of the shaded figure to the area of the

figure that encloses it.

3x

Challenge Simplify each expression. State any excluded values.

48. nr
    m2 + lim n + 10 n2 49.

q2 — 5 ab + 6 b2

a2 + 2 ab — 8 b2 50.

36v2 - 49 w2

18v2 + 9vw - 14 w2

6 6 8 C h a p t e r 11 Rat io nal Expressions and Funct ions