Introduction to Polynomials5.25.2

1. Identify monomials.2. Identify the coefficient and degree of a monomial.3. Classify polynomials.4. Identify the degree of a polynomial.5. Evaluate polynomials.6. Write polynomials in descending order of degree.7. Combine like terms.

Objective 1

Identify monomials.

Monomial: An expression that is a constant, a variable, or a product of a constant and variable(s) that are raised to whole number powers.

Exponent can’t be negative!Exponent can’t have fractions!

a numberx, y

Multiply a number and a

variable

When an equation in one variable is solved the answer is a point on a line.

Is the given expression a monomial?Is the given expression a monomial?

18

34 x

b0.4a– 2

x3

YesYes

No No

Objective 2

Identify the coefficient and degree of a monomial.

Coefficient of a monomial: The numerical factor in a monomial.

Degree of a monomial: The sum of the exponents of all variables in a monomial.

When an equation in one variable is solved the answer is a point on a line.

Identify the coefficient and degree of each monomial:Identify the coefficient and degree of each monomial:

28p

18

m-

276 uv.

532 a 24

C: -1D: 1

C: 8D: 2

C: 18D: 0

C: -6.7D: 3

C: 23 = 8D: 5

C: 16D: 0

x0

Objective 3

Classify polynomials.

Objective 4Identify the degree of a polynomial.

Polynomial: A monomial or an expression that can be written as a sum of monomials.

Examples: 4x, 4x + 8, 2x2 - 5xy + 8y

Polynomial in one variable: A polynomial in which every variable term has the same variable.

Example: x2 – 5x + 2

Binomial: A polynomial containing two terms.

Trinomial: A polynomial containing three terms.

Degree of a polynomial: The greatest degree of any of the terms in the polynomial.

When an equation in one variable is solved the answer is a point on a line.

Identify the type of polynomial and the degree:Identify the type of polynomial and the degree:

24ab

134 3 nn

z9x- 2

49 23 xxx

xy

68 jjjj 142116522 423

MonomialD: 3

BinomialD: 2

TrinomialD: 3

PolynomialD: 3

Not a polynomial PolynomialD: 4

Objective 5

Evaluate polynomials.

Evaluate each of the following:Evaluate each of the following:

y,x for yx 412 2

212 b,a for ba

43 n for nn2

-2(-1)2(4) = -8

(-4)2 – (-4) – 3 = 16 + 4 – 3 = 17

- (-1)2 (2) = - (1)(2) = -2

Objective 6

Write polynomials in descending order of degree.

Combine like terms.

Objective 7

Writing a Polynomial in Descending Order of DegreePlace the highest degree term first, then the next highest degree, and so on.

Write the polynomial in descending order.

2 3 42 5 7 4 x x x x

44x 3x 27x x2 5

Combine like terms and write the resulting polynomial in descending order of degree.

3 2 3 34 6 3 7 4 3 6x x x x x x

5 2 5 26 2 3 1 3 3 a a b b a b a b

38x

532 25 baa

26x x2 4

Slide 5- 18Copyright © 2011 Pearson Education, Inc.

Classify the expression

a) Monomial

b) Binomial

c) Trinomial

d) None of these

2 33 5.x y

5.2

Slide 5- 19Copyright © 2011 Pearson Education, Inc.

Classify the expression

a) Monomial

b) Binomial

c) Trinomial

d) None of these

2 33 5.x y

5.2

Slide 5- 20Copyright © 2011 Pearson Education, Inc.

Evaluate when x = –3.

a) –118

b) –10

c) 10

d) 134

3 23 5 8 x x

5.2

Slide 5- 21Copyright © 2011 Pearson Education, Inc.

Evaluate when x = –3.

a) –118

b) –10

c) 10

d) 134

3 23 5 8 x x

5.2

Slide 5- 22Copyright © 2011 Pearson Education, Inc.

Identify the degree of the polynomial.

a) 3

b) 5

c) 6

d) 7

3 2 4 6 56 5 8 4 x x y x y y

5.2

Slide 5- 23Copyright © 2011 Pearson Education, Inc.

Identify the degree of the polynomial.

a) 3

b) 5

c) 6

d) 7

3 2 4 6 56 5 8 4 x x y x y y

5.2