\fsheik Rahman######################################### #s#h#e#i#k# #R#a#h#m#a#n########s# ##/g#################### ##7######s# ###T#i#m#e#s# #N#e#w# #R#o#m# Factoring Read the following instructions in order to complete this discussion, and review the example of how to complete the math required for this assignment: On pages 3456 and 353 of Elementary and Intermediate Algebra, there are many factoring problems. You will find your assignment in the following table. If the 3rd letter of your last name is On Page 3456 Do the Following On Page 353 Do the Following A or N 80 and 106 68 B or O 72 and 104 38 C or P 98 and 102 64 D or Q 68 and 100 30 E or R 82 and 96 58 F or S 66 and 54 26 G or T 92 and 64 56 H or U 70 and 62 48 I or V 90 and 56 28 J or W 74 and 60 62 K or X 88 and 58 34 L or Y 78 and 52 66 M or Z 86 and 76 36 My 3rd letter of last name H Page 70 Solution a) Since dividing by 5 is equivalent to multiplying by , we have Note that you can simply divide10by5to get2. b ) Since dividing by 2 is equivalent to multiplying by ,we have Note that both 4 and 8 are divided by 2. So we could have written Now do Exercises 53-64 CAUTION It is not correct to divide only one term in the numerator by the denominator. For example, because and 2 + 7 = 9. 4Removing Parentheses In Section 1.7 we used the distributive property to multiply a sum or difference by 1 and remove the parentheses. For example, If 1 is replaced with a negative sign, the parentheses are removed in the same manner because multiplying a number by 1 is equivalent to finding its opposite. So, If a subtraction sign precedes the parentheses, it is removed in the same manner also, because subtraction is defined as addition of the opposite. So, If parentheses are preceded by a negative sign or a subtraction symbol, the signs of all terms within the parentheses are changed when the parentheses are removed. Page 62 EXAMPLE 6 Writing a sum or difference as a product Use the distributive property to factor each expression. a) 7 x 21 b 5a + 5 ) Solution a) b ) Now do Exercises 39-50 4The Identity Properties The numbers 0 and 1 have special properties. Multiplication of a number by 1 does not change the number, and addition of 0 to a number does not change the num ber. That is why 1 is called the multiplicative identity and 0 is called the additive identity. Additive Identity Property For any real number a, Multiplicative Identity Property For any real number a, 5The Inverse Properties The idea of additive inverses was introduced in Section 1.3. Every real number a has an additive inverse or opposite, a , such that a + ( a) = 0. Every nonzero real number a also has a multiplicative inverse orreciprocal, written , such that . Note that the sum of additive inverses is the additive identity and that the product of multiplicative inverses is the multiplicative identity. Additive Inverse Property For any real number a, there is a unique number a such that Multiplicative Inverse Property For any nonzero real number a, there is a unique number Page 48 104. 105. 106. 107. 108. 3(1)2 5(1) + 4 2(1)2 5(1)6 5 22 + 34 5 + (2)232 such that 109. 2 |9 62| 110. 8 3 |5 42 + 1| 111.32 5[4 2(4 9)] 112. 2[(3 4)3 5] + 7 113. 1 5 |5(9 + 1)| 114. |6 37| + |7(5 2)| Use a calculator to evaluate each expression. Round approximate answers to four decimal places. 115. 3.224(3.6)(2.2) 116. (4.5)24(2.8)(4.6) 117. (5.6)3[4.7(3.3)2] 118. 9.83[1.2(4.4 9.6)2] 119. 120. 4Applications Solve each problem. See Example 9. 121. Gambler's ruin. A gambler bets $5 and loses. He doubles his bet and loses again. He continues this pattern, losing eight times in a row. His ninth bet will be 5 2 8 dollars. a.Calculate the amount of the ninth bet. b.What is the total amount lost on the first eight bets? 122. Big profits. Big Bulldog Motorcycles showed a profit of $50,000 in its first year of operation. The company plans to double the profit each year for the next 9 years. a) What will be the amount of the profit in the tenth year? b) What will be the total amount of profit for the first 10 years of business? 123. Population of the United States. In 2009 the population of the United States was 306.2 million (U.S. Census Bureau, www.census.gov). If the popula tion continues to grow at an annual rate of 1.05%, then the population in the year 2020 will be 306.2(1.0105) 11 million. a) Evaluate the expression to find the predicted population in 2020 to the nearest tenth of a million people. Use the accompanying graph to estimate the year in which the population will reach 400 million people. b ) 124. > 125. 126.Figure for Exercise 123 124. Population of Mexico. In 2009 the population of Mexico was 110.3 million. If Mexico's population continues to grow at an annual rate of 1.43%, then the population in 2020 will be 110.3(1.0143)11 million. a) Find the predicted population in 2020 to the nearest tenth of a million people. b) Use the result of Exercise 123 to determine whether the United States or Mexico will have the greater increase in population between 2009 and 2020. Getting More Involved 125. Discussion How do the expressions ( 5)3, (53), 53, ( 5)3, and 1 53 differ? 126. Discussion How do the expressions (4)4, (44), 44, (4)4, and1 44 differ