College Algebra K/DCMonday, 14 September 2015

• OBJECTIVE TSW identify polynomials and their characteristics.

•ASSIGNMENT DUE TOMORROW, 09/15/2015– Sec. R.3: PP. 28-29 (1-9 ALL, 11-22 ALL, 27-37

ALL)

• QUIZ: Mean, Median, Mode, Range, Absolute Value will be tomorrow, 09/15/2015.

2

WS Mean, Median, Mode Answers1) a) 12 5) a) 40.61

b) 13 b) 40.2c) no mode c) 43.4

2) a) 44.08 6) a) 6' 4"b) 42 b) Barry: 6' 4"c) no mode FL So: 6' 4"d) 94 c) Barry's mean

3) height is taller

by 0.09".d) #12, #20, #30

4) a) 83b) median = 66, no mode

25.6

25 19

22.2

14 14

21.2

21 21Pittsburgh Pittsburgh Montreal

New York Montreal Pittsburgh

Montreal New York New York

2-4

PolynomialsSec. R.3:

2-5

Polynomials

• A polynomial is an algebraic expression with a single term or group of terms with only whole-number exponents on the variable.

polynomials not polynomials

2x2 + 3x

5x 4

10 (can be written as 10x0)

2 69 4x x

x

x

47x1

52x

2-6

Polynomials

• The degree of a polynomial is the highest exponent.

4x3 2x2 3x + 7 Degree = 3

5y4 + 2y3 + y 6 Degree = 6

• If a polynomial has more than one variable, the degree is the largest sum of the exponents for any one term.

14a4b3 + 9a7b – 4ab4 Degree = 8

2-7

Polynomials

• The coefficient of a term is the number in front of the variable.

13x 3 coefficient is –13

x 4 coefficient is 1

2-8

Polynomials

• The leading coefficient of a polynomial is the coefficient with the term of the highest degree.

4x 3 6x 2 + 8x + 10 leading coefficient is 4

2-9

Properties of Exponents

n a a aa a

n times

r m r ma a a

rmr ma a

r r

r

a

b

a

b

and1

rr

r

r r

a ba

ba a

0 1, 0a a

10

Find each product.

Using the Product Rule

(a)

(b)Commutative and associative properties

Product rule

11

(a)

Simplify. Assume all variables represent nonzero real numbers.

Using the Power Rules

(b)

12

Simplify. Assume all variables represent nonzero real numbers.

Using the Power Rules

(c)

(d)

13

Simplify. Assume all variables represent nonzero real numbers.

Using the Power Rules

24 7 3( 2) 2e x x 2 24 7 32 2 x x

4 14 62 2 x x

4 14 1 62 x

18 72 x

2-14

Using the Definition of a0

Evaluate each power.

(a) 80 = 1

(b) –80 = –1

(c) (–8)0 = 1

(d) –(– 8)0 = –1

(e) (–3b8)0 = 1, b ≠ 0

Today’s Assignment (Monday, 09/14/15)

• Sec. R.3: PP. 28-29 (1-9 ALL, 11-22 ALL, 27-37 ALL)– This assignment is due tomorrow, 15 September

2015.

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