Please Show Your Work
Section 4.2
Exercise 84
Computations with Scientific Notations
Perform the computations. Write answers in scientific notation.
= (9/3) * 10-4 - (-6) = 3 * 102
Exercise 114
Solve. Diameter of a circle.
If the diameter of a circle is
meters, then what is its radius?
Radius = Diameter / 2 = (1.3 * 10-12)/ 2 = 0.65 * 10-12 = 6.5 * 10-13
Section 4.3
Exercise 94
Solve. 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.
P(x) = 2(2x - 5) + 2(3x + 9) = 4x - 10 + 6x + 18 = 10x + 8
P(4) = 10(4) + 8 = 40 + 8 = 48
Exercise 98
Solve. Height difference.
A red ball and a green ball are simultaneously tossed into the air. The red ball is given an initial
velocity of 96 feet per second, and its height t seconds after it is tossed is
feet. The
green ball is given an initial velocity of 80 feet per second, and its height t seconds after it is
tossed is
feet.
a) Find a polynomial D(t) that represents the difference in the heights of the two balls.
D(t) = (-16t2 + 96t) - (-16t2 + 80t) = 96t - 80t = 16t
b) How much higher is the red ball 2 seconds after the balls are tossed?
D(2) = 16(2) = 32 feet
c) In reality, when does the difference in the heights stop increasing?
The difference in the heights will stop increasing when the green ball
returns to the ground.
Section 4.4
Exercise 78
Solve. 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).
A(x) = (2x - 1)(x + 2) = 2x2 + 4x - x - 2 = 2x2 + 3x - 2
A(5) = 2(5)2 + 3(5) - 2 = 2(25) + 15 - 2 = 63
Exercise 86
Solve. Selling shirts.
If a vendor charges p dollars each for rugby shirts, then he expects to sell 2000-100p shirts at a
tournament.
a) Find a polynomial R(p) that represents the total revenue when the shirts are p dollars each.
R(p) = (2000 - 100p)(p) = 2000p - 100p2
b) Find R(5), R(10), and R(20).
R(5) = 2000(5) - 100(5)2 = 10,000 - 2,500 = $7,500
R(10) = 2000(10) - 100(10)2 = 20,000 - 10,000 = $10,000
R(20) = 2000(20) - 100(20)2 = 40,000 - 40,000 = $0
c) Use the bar graph to determine the price that will give the maximum total revenue.
(The ten goes all the way up to ten, everything else is in halves)
Maximum revenue occurs at a price of $10
Section 4.5
Exercise 52
Multiplying Binomials Quickly
Find each product. Try to write only the answer.
= 9h2 - 25
Exercise 98
Solve. Area of a parallelogram.
Find a trinomial A(x) that represents the area of a parallelogram whose base is 3x+2 meters and
whose height is 2x+3 meters. Find A(3).
A(x) = (3x+2)(2x+3) = 6x2 + 13x + 6
A(3) = 6(3)2 + 13(3) + 6 = 6(9) + 39 + 6 = 54 + 45 = 99
Section 4.6
Exercise 88
Applications
Solve. Area of a square.
Find a polynomial A(x) that represents the area of the shaded region in the accompanying figure.
A(x) = (x-3)(x-3) = x2 - 6x + 9
Exercise 96
Applications
Solve. Compound semiannually.
P dollars is invested at annual interest rate r for 1 year. If the interest is compounded
semiannually, then the polynomial
represents the value of the investment after 1 year.
Rewrite this expression without parentheses. Evaluate the polynomial if P=$200 and r=10%.
P(1 + r/2)2 = P(1+r/2)(1+r/2) = P(1 + r + r2/4) = P + Pr + Pr2/4
For P= 200 and r= 10%, the value is 200 + 200(0.10) + 200(0.10)2/4 = $220.50
Section 4.7
Exercise 66
Dividing a Polynomial by a Binomial
Write each expression in the form:
= x + 4/2x
= x + 2/x
Exercise 88
Solve. 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.
2L + 2x = 6x + 6
2L = 6x - 2x + 6
2L = 4x + 6
L = 2x + 3
Section 5.1
Exercise 40
Greatest Common Factor for Monomials
Find the greatest common factor for each group of monomials.
16x2z = 24x2z
40xz2 = 23 * 5 xz2
72z3 = 23 * 32 * z3
The GCF is 23z = 8z
Exercise 68
Factor out the GCF in each expression.
= 3xy(5xy - 3y + 2x)
Exercise 72
Factor out the GCF in each expression.
= (a+1)(a-3)
Section 5.2
Exercise 16
Factoring a Difference of Two Squares
Factor each polynomial.
= (3a - 8b)(3a + 8b)
Exercise 62
Factoring Completely
Factor each polynomial completely.
= xy(x2 + 2xy + y2)
= xy(x + y)(x + y)
= xy(x + y)2
Exercise 80
Factoring by Grouping
Use grouping to factor each polynomial completely.
= x(x2 + a) + 3(x2 + a) = (x + 3)(x2 + a)
Section 5.3
Exercise 58
Factor each polynomial. If the polynomial is prime, say so.
= (z + 15)(z + 3)
Exercise 64
Factoring with Two Variables
Factor each polynomial.
Polynomial is prime.
Exercise 102
Factoring Completely
Factor each polynomial completely. If the polynomial is prime, say so.
= 3xy2(x2 - x + 1)
Section 5.4
Exercise 18
Factor each trinomial using the ac method.
ac = 2(5) = 10
Factors of 10 that add to 11 are 10 and 1
2x2 + 1x + 10x + 5
x(2x + 1) + 5(2x + 1)
(x + 5)(2x + 1)
Exercise 26
Factor each trinomial using the ac method.
ac = 21(3) = 63
Factors of 63 that have a difference of 2 are 9 and 7
21x2 + 9x - 7x - 3
3x(7x + 3) - 1(7x + 3)
(3x - 1)(7x + 3)
Section 5.5
Exercise 36
Factoring a Difference of Two Fourth Powers
Factor each polynomial completely.
= (m2 + n2)(m2 - n2)
= (m2 + n2)(m + n)(m - n)
Exercise 44
The Factoring Strategy
Factor each polynomial completely. If a polynomial is prime, say so.
= 3x(x2 - 4)
= 3x(x+2)(x-2)
Section 5.6
Exercise 18
The Zero Factor Property
Solve by factoring.
(2h - 3)(h + 1) = 0
2h - 3 = 0
h+1=0
2h = 3
h = -1
h = 3/2
Exercise 32
Solve each equation.
8w2 + 2w - 1 = 0
(4w - 1)(2w + 1) = 0
4w - 1 = 0
2w + 1 = 0
4w = 1
2w = -1
w = 1/4
w = -1/2