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# Algebra problems

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Factor out the GCF in each expression.

59. 2x^3-6x^2+8x

60. 6x^3+18x^2-24x

*61. 12x^4t+30x^3t-24x^2t^2

*62. 15x^2y^2-9xy^2+6x^2y

Factor each polynomial completely.
60. 32x^2y-2y^3

61. 3ab^2-18ab+27a

Use grouping to factor each polynomial completely.
66. 3x+3z+ax+az

67. x^3+x^2-4x-4

90. Demand for pools. Tropical Pools sells an above-ground model for p dollars each.
The monthly revenue from the sale of this model is a function of the price, given by
R = -0.08p^2 + 300p.
Revenue is the product of the price p and the demand (quantity sold).
a) Factor out the price on the right-hand side of the formula.

b) What is an expression for the monthly demand?

c) What is the monthly demand for this pool when the price is \$3000?

d) Use the graph (to the right) to estimate the price at which the revenue is maximized.
Approximately how many pools will be sold monthly at this price?

e) What is the approximate maximum revenue?

f) Use the graph (to the right) to estimate the price at which the revenue is zero.

Factor each polynomial completely.
67. w^2-18w+81

68. w^2+30w+81

79. 6x^3y+30x^2y^2+36xy^3

80. 3x^3y^2-3x^2y^2+3xy^2

Factor each polynomial completely.
81. 12t^4-2t^3-4t^2

82. 12t^3+14t^2+4t

85. -4w^2+7w-3

86. -30w^2+w+1

90. Worker efficiency. In a study of worker efficiency at Wong Laboratories it was found that the number of components
assembled per hour by the average worker t hours after starting work could be modeled by the function.
N(t)= -3t^3+23t^2+8t

a) rewrite the formula by factoring the right-hand side completely.

b) Use the factored version of the formula to find N(3).

c) Use the graph to estimate the time at which the workers are most efficient.

d) Use the graph to estimate the maximum number of components assembled per hour during an 8 hour shift.

35-60 Factor each polynomial completely. If a polynomial is prime say so.

35. 5max^2+20ma

*37. 9x^2+6x+1

*38. 9x^2+6x+3

40. 5x^2y^2-xy^2-6y^2

*50. a^2-25a

*60. m^4n+mn^4

78. Decreasing cube. Each of the three dimensions of a cube with a volume of y^3 cubic centimeters is decreased by a whole number of centimeters. If the new volume is y^3-13y^2+54y-72 cubic centimeters and the new width is y-6 centimeters, then what are the new length and height?

Find the LCD for the given rational expressions, and convert each rational expression into an equivalent rational expression
with the LDC as the denominator.

Reduce each answer to lowest terms.

See the attached file for details

Some problems scanned others typed in.
When ^ is used in a problem it means the next number is an exponent, an example is 3^3 which is the same as 3 to the 3rd power.