© copyright by houghton mifflin company. all rights reserved.1 monomials & polynomials define...

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© Copyright by Houghton Mifflin Company. All rights reserved. 1 Monomials & Polynomials Define monomials and polynomials. Determine the degree of a polynomial. Describe a function using function notation. Evaluate a polynomial for a given value of the variable

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Page 1: © Copyright by Houghton Mifflin Company. All rights reserved.1 Monomials & Polynomials Define monomials and polynomials. Determine the degree of a

© Copyright by Houghton Mifflin Company. All rights reserved. 1

Monomials & Polynomials

Define monomials and polynomials.

Determine the degree of a polynomial.

Describe a function using function notation.

Evaluate a polynomial for a given value of the variable

Page 2: © Copyright by Houghton Mifflin Company. All rights reserved.1 Monomials & Polynomials Define monomials and polynomials. Determine the degree of a

© Copyright by Houghton Mifflin Company. All rights reserved. 2

Monomials

A monomial has:

524 zxy

One or more variables multiplied together

nonnegative, integer exponents

No addition or subtraction

Coefficient

Page 3: © Copyright by Houghton Mifflin Company. All rights reserved.1 Monomials & Polynomials Define monomials and polynomials. Determine the degree of a

© Copyright by Houghton Mifflin Company. All rights reserved. 3

Monomials

Examples of monomials

x3

zyx 222

5 The degree of a monomial is the sum of the exponents of the variables.

Degree = 1

Degree = 2+2+1=5

Degree = 0

Page 4: © Copyright by Houghton Mifflin Company. All rights reserved.1 Monomials & Polynomials Define monomials and polynomials. Determine the degree of a

© Copyright by Houghton Mifflin Company. All rights reserved. 4

Polynomials

A polynomial is a sum or difference of monomials.

2x235 2 xx

7432 234 yxyyx

Page 5: © Copyright by Houghton Mifflin Company. All rights reserved.1 Monomials & Polynomials Define monomials and polynomials. Determine the degree of a

© Copyright by Houghton Mifflin Company. All rights reserved. 5

Polynomials

The degree of a polynomial is the degree of the monomial with the highest degree.

2x

235 2 xx7432 234 yxyyx

Degree =1

Degree = 2

Degree = 7

Page 6: © Copyright by Houghton Mifflin Company. All rights reserved.1 Monomials & Polynomials Define monomials and polynomials. Determine the degree of a

© Copyright by Houghton Mifflin Company. All rights reserved. 6

Evaluating Polynomials

To evaluate a polynomial for a given value of the variable, substitute the given value for the variable.

Evaluate the polynomial for x = -3.

3 27 16 5 3x x x 3 27( 3) 16( 3) 5( 3) 3

315

Page 7: © Copyright by Houghton Mifflin Company. All rights reserved.1 Monomials & Polynomials Define monomials and polynomials. Determine the degree of a

© Copyright by Houghton Mifflin Company. All rights reserved. 7

Addition and Subtraction

Adding polynomials.Subtracting polynomials.

Page 8: © Copyright by Houghton Mifflin Company. All rights reserved.1 Monomials & Polynomials Define monomials and polynomials. Determine the degree of a

© Copyright by Houghton Mifflin Company. All rights reserved. 8

Adding Polynomials

Like terms of polynomials are monomials with the same variables with the same exponents. xyyxxyyx 625 22

Like Terms

Page 9: © Copyright by Houghton Mifflin Company. All rights reserved.1 Monomials & Polynomials Define monomials and polynomials. Determine the degree of a

© Copyright by Houghton Mifflin Company. All rights reserved. 9

583126 232 xxxxx

Adding Polynomials

To add polynomials, combine like terms.Add:

583 and 126 232 xxxxx

)583()126( 232 xxxxx

33x 22x 4x3

No other like termAdd 6x2 + (-8x2)Add 2x + xAdd –1 + 5

Page 10: © Copyright by Houghton Mifflin Company. All rights reserved.1 Monomials & Polynomials Define monomials and polynomials. Determine the degree of a

© Copyright by Houghton Mifflin Company. All rights reserved. 10

Subtracting Polynomials

To subtract polynomials, combine like terms.Subtract:

7595 and 472 2323 xxxxx

)7595()472( 2323 xxxxxRemove parenthesis. Notice that the sign of every term in the second parenthesis changes

7595472 2323 xxxxx

Page 11: © Copyright by Houghton Mifflin Company. All rights reserved.1 Monomials & Polynomials Define monomials and polynomials. Determine the degree of a

© Copyright by Houghton Mifflin Company. All rights reserved. 11

Subtracting Polynomials

7595472 2323 xxxxx

Combine like terms:

35167 23 xxx

)7595()472( 2323 xxxxx

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