Intermediate Algebra (11th edition)

23.Concept Check When asked to factor , a student gave the fol-
lowing incorrect answer:. WHAT WENT WRONG?What is
the correct answer?

24.If the area of this rectangle is represented by , what
is the width in terms of p?

4 p^2 + 3 p- 1

x^21 y^2 - 62 + 51 y^2 - 62

x^2 y^2 - 6 x^2 + 5 y^2 - 30

CHAPTER 6 Review Exercises 357

4 p – 1

51.A triangular wall brace has the shape of
a right triangle. One of the perpendicu-
lar sides is 1 ft longer than twice the
other. The area enclosed by the triangle
is 10.5. Find the shorter of the per-
pendicular sides.

52.A rectangular parking lot has a length 20 ft more than its width. Its area is 2400. What are the dimensions of the lot?

ft^2

Solve each problem.

The area is 10.5 ft^2.

2 x + 1

x W

W + 20

The area is 2400 ft^2.

6.3 Factor completely.

25. 26. 27.

28. 29. 30.

31. 32. 33.

34.x^2 + 6 x+ 9 - 25 y^2 35. 1 a+b 23 - 1 a-b 23 36.x^5 - x^3 - 8 x^2 + 8

125 x^3 - 1 m^6 - 1 x^8 - 1

x^2 + 14 x+ 49 9 k^2 - 12 k+ 4 r^3 + 27

16 x^2 - 25 9 t^2 - 49 36 m^2 - 25 n^2

6.5 Solve each equation.

37. 38. 39.

40. 41. 42.

43. 44.

45. 46.

47. 48.

49.-x^3 - 3 x^2 + 4 x+ 12 = 0 50. 1 x+ 2215 x^2 - 9 x- 182 = 0

1 x+ 221 x- 22 = 1 x- 221 x+ 32 - 2 2 x^3 - x^2 - 28 x= 0

6 x^2 + 9 x= 0 12 x+ 121 x- 22 =- 3

8 x^2 + 14 x+ 3 = 0 - 4 x^2 + 36 = 0

x^2 + 2 x= 8 6 x^2 = 5 x+ 50 6 x^2 + 7 x= 3

x^2 - 8 x+ 16 = 0 15 x+ 221 x+ 12 = 0 x^2 - 5 x+ 6 = 0

A rock is projected directly upward from ground level. After t seconds, its height ( if air
resistance is neglected) is given by

53.After how many seconds will the rock return to the ground?

54.After how many seconds will it be 240 ft above the ground?

55.Why does the question in Exercise 54have two answers?

56.After how many seconds does the rock reach its maximum height, 1024 ft?

ƒ 1 t 2 =- 16 t 2 + 256 t.

Solve each equation for the specified variable.

for k 58.z= for w

3 w+ 7 w 3 s+bk=k- 2 t