6.1 polynomial functions. monomials a monomial is a number, a variable or the product of both

6.1 Polynomial Functions

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6.1

Polynomial Functions

Monomials

A monomial is a number, a variable or the product of both.

Examples of monomials

715

xyzyx

Page 4: 6.1 Polynomial Functions. Monomials A monomial is a number, a variable or the product of both

The degree of a monomial

The degree of a monomial is the exponents added together

Page 5: 6.1 Polynomial Functions. Monomials A monomial is a number, a variable or the product of both

Find the degree

715

xyzyx

Polynomial Functions

011

1 ...)( axaxaxaxP nn

A polynomial function is any function in the form of:

It is defined as a monomial or a sum of monomials

Page 7: 6.1 Polynomial Functions. Monomials A monomial is a number, a variable or the product of both

Things to know

• The degree of a polynomial is the largest exponent

• Standard form of a polynomial is written from highest exponent to lowest

• The leading coefficient is the coefficient on the term with the highest degree

Page 8: 6.1 Polynomial Functions. Monomials A monomial is a number, a variable or the product of both

Picking apart a polynomial

2014935)( 234 xxxxxP

Leading coefficient

Degree

Page 9: 6.1 Polynomial Functions. Monomials A monomial is a number, a variable or the product of both

Write the polynomial in standard form. Then find the degree and

leading coefficient

954 41312)( xxxxP

Page 10: 6.1 Polynomial Functions. Monomials A monomial is a number, a variable or the product of both

Degree

Name using degree

Polynomial Example Number of terms

Name using number of

terms

Page 11: 6.1 Polynomial Functions. Monomials A monomial is a number, a variable or the product of both

Degree

Name using degree

Polynomial Example Number of terms

Name using number of

terms

11915 3 xx

14193 324 xxx

x12

83 2 x

53 915 xx

Fill in the blanks

Page 12: 6.1 Polynomial Functions. Monomials A monomial is a number, a variable or the product of both

Homework

12/6: #42 pg 309 1-12, 35-57 odd

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