Download Use the five properties of exponents to simplify each

Use the five properties of exponents to simplify each of the following expressions.
70. 2x 2 - 5x + 1, x=2 and x = -2
2(2)2-5(2)+1=8-10+1=-1
2(-2)2-5(-2)+1=8-10+1=-1
106. 106. Business and finance. The cost, in dollars, of making suits is described as 20 times
the number of suits plus 150. Use s as the number of suits and write a polynomial to
describe this cost. Find the cost of making seven suits.
C=20s+150
C=20(7)+150=140+150=$290
Simplify the following expressions. Write your answers with positive exponents only.
52.
(m 4 ) 3 m-12 -4 1
= -8 =m = 4
m
(m  2 ) 4 m
Write your result in scientific notation.
76.
4.5 X 1012
3x105
1.5 X 10 7
83. Science and medicine. Megrez, the nearest of the Big Dipper stars, is
17
6.6 X 10 m from the Earth. Approximately how long does it take light, traveling
16
at 10 m/year, to travel from Megrez to the Earth?
6.6x1017
=6.6x10=66 years
1016
84. Science and medicine. (using the information from #83)Alkaid, the most distant star in the Big
18
Dipper, is 2.1 X 10 m from the Earth. Approximately how long does it take light to travel
from Alkaid to the Earth?
2.1x1018
=2.1x102=210 years
1016
Remove the parentheses in the following expressions and simplify when possible.
22. 10m - (3m - 2n)=10m-3m+2n=7m+2n
Subtract:
2
2
36. 7y – 3y from 3y - 2y
3y2-2y -(7y-3y2)=3y2-2y-7y+3y2=6y2-9y=3y(2y-3)
Add, using the vertical method.
2
2
48. 3x - 4x – 2, 6x-3, and 2x + 8=5x2+2x+3
Multiply
28. (b+7)(b+5)=b2+12b+35
32. (s-12)(s-8)=s2-20s+96
Multiply, using the vertical method.
2
2
64. (m+3n)(m - 3mn + 9n )=3m2n-9mn2+27n3+m3-3m2n+9mn2=m3+27n3
Multiply
70. 6m(3m – 2)(3m – 7)=6m(9m2-27m+14)=54m3-162m2+84m
Find each of the following squares.
2
14. (3a – 4b) =9a2-24ab-16b2
Find the following products
38. 5w(2w – z)(2w + z)=5w(4w2-z2)=20w3-5wz2
Divide
2 x 4 y 4 z 4  3x 3 y 3 z 3  xy 2 z 3
20.
=2x3y2z+3x2y-1
xy 2 z 3
Perform the indicated divisions.
26.
3x 2  17 x  12
=3x+1-18/(x+6)
x6
x 2  18 x  2 x 3  32
38.
=2x2-7x+10-8/(x+4)
x4
x 4  x 2  16 3 2
40.
=x -2x +5x-10+4/(x+2)
x2
Find the greatest common factor.
12. 9b
3
, 6b 5 , 12b 4 =3b3
Factor the polynomials.
2
2
44. 3ab +6ab – 15a b=3ab(b+2-5a)
Find the GCF of each product
58. (5b-10) (2b+4)=5(b-2)(2)(b+2)=10(b-2)(b+2)
64. 64. Number problem. If we could make a list of all the prime numbers, what number
would be at the end of the list? Because there are an infinite number of prime numbers,
there is no “largest prime number.” But is there some formula that will give
us all the primes? Here are some formulas proposed over the centuries:
2
n + n + 17
2n 2 + 29 n 2 - n + 11
In all these expressions, n= +1, 2, 3, 4, . . . , that is, a positive integer beginning
with 1. Investigate these expressions with a partner. Do the expressions give prime
numbers when they are evaluated for these values of n? Do the expressions give
every prime in the range of resulting numbers? Can you put in any positive number
for n?
Factor the following trinomials completely.
2
26. s - 4s – 32=(s-8)(s+4)
54. 4s 20 s t  96 s t =4s2(s2-5st-24t2)=4s2(s+3t)(s-8t)
4
3
2 2
Find all positive values for k for which each of the following can be factored
2
64. X + 5x + k
Factor the following polynomials completely
2
50. 24x - 18x – 6=6(4x2-3x-1)=6(4x+1)(x-1)
2
68. 12 + 4a – 21a =(6-7a)(2+3a)
Factor the binomials.
2
2
26. 64m - 9n =(8m-3n)(8m+3n)
Determine whether the following trinomials is a perfect square. If it is, factor the
trinomial
2
46. X + 10x + 25=(x+5)2
Factor the following trinomials
2
2
56. 9w - 30wv + 25v =(3w-5y)2
Factor the expression
3
2
62. 3a (2a+b) – 27ab (2a+b)=(2a+b)(3a3-27ab2)=3a(2a+b)(a2-9b2)=3a(2a+b)((a+3b)(a-3b)
3
66. Find a value for k so that 20a b -kab
2a + 3.
3
will have the factors 5ab, 2a - 3b, and
Factor each polynomial by grouping the first two terms and the last two terms.
5
3
2
6. x + x - 2x - 2
(x5+x3)-(2x2+2)=x3(x2+1)+2(x2+1)=(x3+2)(x2+1)
Factor each polynomial completely by factoring out any common factors and then factor by
grouping. Do not combine like terms.
4
3
3
2
2
18. 2p + 3p q – 2p q – 3p q =p2(2p2+pq-3q2)=p2(2p+3q)(p-q)
Section 4.8
pp. 408-409
22, 50
Use the ac test to determine which of the following trinomials can be factored. Find the
values of m and n for each trinomial that can be factored.
2
26. x - x + 2=(x+1)(x-2)
2
28. 3x - 14x – 5
Rewrite the middle term as the sum of two terms and then factor completely
2
70. 8x - 6x – 9=(4x+3)(2x-3)
4
3
102. 20n - 22n - 12n
2
Factor each polynomial completely. To begin, state which method should be applied as the
first step. Then continue the exercise and factor each polynomial completely
2
12. 3x + 6x – 5xy – 10y=3x(x+2)-5y(x+2)=(x+2)(3x-5y)
3
2
26. 12b - 86b + 14b=2b(6b2-43b+7)=2b(b-7)(6b-1)
Factor:
2
34. 12(x+1) - 17(x+1) + 6=(x+1)[12(x+1)-17]=(x+1)(12x+12-17)=(x+1)(12x-5)
Solve the following quadratic equations
2
22. 5x + 2x = 3
5x2+2x-3=0
(x-1)(x+3)=0
x=1,-3
50. Business and finance. The relationship between the number of calculators x that
a company can sell per month and the price of each calculator p is given by
x = 1700 - 100p. Find the price at which a calculator should be sold to produce a
monthly revenue of $7000. (Hint: Revenue = xp.)
x=1700-100p
revenue=xp
7000=xp
x=7000/p
7000/p=1700-100p
7000=1700p-100p2
100p2-1700p+7000=0
p2-17+70=0
(p-7)(p-10)=0
p=7,10