4.1
Simplify. All variables represent nonzero real numbers.
50) _5y4(y5)2
------=
15y7(y2)3
66) (3y8)4
2zy2
Simplify. All variables represent nonzero real numbers
72. ( 33)3
( 3)
4.2
Simplify
40. w(-4) parenthesis are exponents
W(6)
58. (2s(-1)t(3))(-3) parenthesis are exponents
(6s(2)t(-4))
68. 9.3 x 10(-5)= 0.000093
Perform the computations.Write answers in scientific notation.
84. 9 x 10 (-4) parentheses are exponents
3 x 10 (-6)
4.3
32. Evaluate -2x4 - 3x2 + 5x -9 for x = 2. (small numbers are exponents)
-43
64. (4 - 5y + y3) -(2 - 3y + y2)= (small numbers are exponents)
94) Perimeter of a rectangle. The width of a rectangular playground
is 2x - 5 feet, and the length is 3x + 9 feet. Write a
polynomial P(x) that represents the perimeter and then
evaluate this perimeter polynomial if x is 4 feet.
Evaluated at 4 gives
4.4
Use the distributive property to find each product
34. (3c2d - d3 + 1)8cd2 (small 2 and 3 are exponent)
78. Swimming space. The length of a rectangular swimming
pool is 2x -1 meters, and the width is x + 2 meters. Write
a polynomial A(x) that represents the area. Find A(5).
86. Selling shirts. If a vendor charges p dollars each for
rugby shirts, then he expects to sell 2000 - 100p shirts at
a tournament.
4.5
Use FOIL to find each product
40. (5y3w2 + z)(2y3w2 +3z) (small numbers are exponents)
4.6
Find each product
48. (3y2 +1)(3y2 - 1) (small numbers are exponents)
78.( 2y - 1)2
( 3 2 ) (small number are exponents)
96) Compounded semiannually. P dollars is invested at annual
rate r for 1 year. If the interest is compounded
semiannually, then the polynomial P(1+r/2)2- (2being the exponent)
represents the
value of the investment after 1 year. Rewrite this expression
without parentheses. Evaluate the polynomial if
P = $200 and r = 10%.
4.7
Find each quotient.
24. -12z10y2
-2z4y2
Write each expression in the form quotient+ remainder
divisor
66. 2x2+4
2x
88. Perimeter of a rectangle. The perimeter of a rectangular
backyard is 6x + 6 yards. If the width is x yards, find a
binomial that represents the length.
5.2 (small numbers are exponents)
Factor each polynomial
16. 9a2-64b2
Factor each polynomial completely
62. x3y +2x2y2 + xy3
Use grouping to factor each polynomial completely
80. x3 + ax + 3a + 3x2
100. Demand for pools. Tropical Pools sells an aboveground
model for p dollars each. The monthly revenue for this
model is given by the formula
R(p)= -0.08p2 +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) Write a formula D(p) for the monthly demand.
c) Find D(3000).
d) Use the accompanying graph to estimate the price at
which the revenue is maximized. Approximately how
many pools will be sold monthly at this price?
No graph here. But the maximum is at p=1875.
e) What is the approximate maximum revenue?
$281,250
f) Use the accompanying graph to estimate the price at
which the revenue is zero.
No graph, but the revenue is 0 when price = 0 and when price = $3,750.