6.1 Polynomial Functions. Monomials A monomial is a number, a variable or the product of both.
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Transcript of 6.1 Polynomial Functions. Monomials A monomial is a number, a variable or the product of both.
![Page 1: 6.1 Polynomial Functions. Monomials A monomial is a number, a variable or the product of both.](https://reader035.fdocuments.in/reader035/viewer/2022062807/5697c0241a28abf838cd4705/html5/thumbnails/1.jpg)
6.1
Polynomial Functions
![Page 2: 6.1 Polynomial Functions. Monomials A monomial is a number, a variable or the product of both.](https://reader035.fdocuments.in/reader035/viewer/2022062807/5697c0241a28abf838cd4705/html5/thumbnails/2.jpg)
Monomials
A monomial is a number, a variable or the product of both.
![Page 3: 6.1 Polynomial Functions. Monomials A monomial is a number, a variable or the product of both.](https://reader035.fdocuments.in/reader035/viewer/2022062807/5697c0241a28abf838cd4705/html5/thumbnails/3.jpg)
Examples of monomials
2
5
2
715
x
xyzyx
![Page 4: 6.1 Polynomial Functions. Monomials A monomial is a number, a variable or the product of both.](https://reader035.fdocuments.in/reader035/viewer/2022062807/5697c0241a28abf838cd4705/html5/thumbnails/4.jpg)
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.](https://reader035.fdocuments.in/reader035/viewer/2022062807/5697c0241a28abf838cd4705/html5/thumbnails/5.jpg)
Find the degree
2
5
2
715
x
xyzyx
![Page 6: 6.1 Polynomial Functions. Monomials A monomial is a number, a variable or the product of both.](https://reader035.fdocuments.in/reader035/viewer/2022062807/5697c0241a28abf838cd4705/html5/thumbnails/6.jpg)
Polynomial Functions
011
1 ...)( axaxaxaxP nn
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.](https://reader035.fdocuments.in/reader035/viewer/2022062807/5697c0241a28abf838cd4705/html5/thumbnails/7.jpg)
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.](https://reader035.fdocuments.in/reader035/viewer/2022062807/5697c0241a28abf838cd4705/html5/thumbnails/8.jpg)
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.](https://reader035.fdocuments.in/reader035/viewer/2022062807/5697c0241a28abf838cd4705/html5/thumbnails/9.jpg)
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.](https://reader035.fdocuments.in/reader035/viewer/2022062807/5697c0241a28abf838cd4705/html5/thumbnails/10.jpg)
Degree
Name using degree
Polynomial Example Number of terms
Name using number of
terms
0
1
2
3
4
5
![Page 11: 6.1 Polynomial Functions. Monomials A monomial is a number, a variable or the product of both.](https://reader035.fdocuments.in/reader035/viewer/2022062807/5697c0241a28abf838cd4705/html5/thumbnails/11.jpg)
Degree
Name using degree
Polynomial Example Number of terms
Name using number of
terms
11915 3 xx
14193 324 xxx
x12
7
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.](https://reader035.fdocuments.in/reader035/viewer/2022062807/5697c0241a28abf838cd4705/html5/thumbnails/12.jpg)
Homework
12/6: #42 pg 309 1-12, 35-57 odd