# Polynomials: a problem book by E. J. Barbeau

By E. J. Barbeau

The e-book extends the highschool curriculum and gives a backdrop for later learn in calculus, smooth algebra, numerical research, and intricate variable idea. routines introduce many suggestions and issues within the concept of equations, similar to evolution and factorization of polynomials, answer of equations, interpolation, approximation, and congruences. the speculation isn't really handled officially, yet relatively illustrated via examples. Over three hundred difficulties drawn from journals, contests, and examinations try out realizing, ingenuity, and talent. every one bankruptcy ends with an inventory of tricks; there are solutions to the various workouts and ideas to all the difficulties. additionally, sixty nine "explorations" invite the reader to enquire study difficulties and comparable issues.

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**Extra info for Polynomials: a problem book**

**Example text**

A. 5 и 8 b. 7(2) each of the following products: a. 7 и 9 SOLUTION b. 4(6) Applying the commutative property to each expression, we have: a. 7 и 9 ϭ 9 и 7 EXAMPLE 12 b. 4(6) ϭ 6(4) Use the associative property of multiplication to rewrite each of the following products: a. (2 и 7) и 9 SOLUTION 11. Use the commutative property b. 3 и (8 и 2) Applying the associative property of multiplication, we regroup as 12. Use the associative property of multiplication to rewrite each of the following products.

7,406 Ϫ 3,405 EXAMPLE 1 SOLUTION Subtract: 376 Ϫ 241 We write the problem vertically, aligning digits with the same place value. Then we subtract in columns. 376 Ϫ 241 m888 Subtract the bottom number in each column from the number above it 135 2. a. Subtract 405 from 6,857. b. Subtract 234 from 345. EXAMPLE 2 SOLUTION Subtract 503 from 7,835. In symbols this statement is equivalent to 7,835 Ϫ 503 To subtract we write 503 below 7,835 and then subtract in columns. 7 , Ϫ 7 , 3 , 5 5 , 0 , 3 3 , 3 , 2 5Ϫ3ϭ2 3Ϫ0ϭ3 8Ϫ5ϭ3 7Ϫ0ϭ7 m8 m88888 m8888888888 m888888888888888 Answers 1.

Some involve addition as well. Be sure to read each problem carefully. 69. Checkbook Balance Diane has $504 in her checking 70. Checkbook Balance Larry has $763 in his checking account. If she writes ﬁve checks for a total of $249, account. If he writes a check for each of the three bills how much does she have left in her account? listed below, how much will he have left in his account? 71. Home Prices In 1985, Mr. Hicks paid $137,500 for his Item Amount Rent Phone Car repair $418 25 117 72. Oil Spills In March 1977, an oil tanker hit a reef off home.