![Page 1: 3.2 Introduction to Polynomials. Identify Monomials Monomial or Term: An expression that is a constant or a product of a constant and variables that are](https://reader036.vdocuments.mx/reader036/viewer/2022062315/5697c0241a28abf838cd46fe/html5/thumbnails/1.jpg)
3.2Introduction to Polynomials
![Page 2: 3.2 Introduction to Polynomials. Identify Monomials Monomial or Term: An expression that is a constant or a product of a constant and variables that are](https://reader036.vdocuments.mx/reader036/viewer/2022062315/5697c0241a28abf838cd46fe/html5/thumbnails/2.jpg)
Identify Monomials
Monomial or Term: An expression that is a constant or a product of a constant and variables that are raised to whole number powers.
![Page 3: 3.2 Introduction to Polynomials. Identify Monomials Monomial or Term: An expression that is a constant or a product of a constant and variables that are](https://reader036.vdocuments.mx/reader036/viewer/2022062315/5697c0241a28abf838cd46fe/html5/thumbnails/3.jpg)
Determine whether the expression is a
monomial5x
-4xy3
X6
8
![Page 4: 3.2 Introduction to Polynomials. Identify Monomials Monomial or Term: An expression that is a constant or a product of a constant and variables that are](https://reader036.vdocuments.mx/reader036/viewer/2022062315/5697c0241a28abf838cd46fe/html5/thumbnails/4.jpg)
Determine whether the expression is a
monomial
5x
-4xy3
X6
8
Yes
Yes
Yes
Yes
Monomial or Term: An expression that is a constant or a product of a constant and variables that are
raised to whole number powers.
![Page 5: 3.2 Introduction to Polynomials. Identify Monomials Monomial or Term: An expression that is a constant or a product of a constant and variables that are](https://reader036.vdocuments.mx/reader036/viewer/2022062315/5697c0241a28abf838cd46fe/html5/thumbnails/5.jpg)
The following are NOT monomials
5/xy
3x2 + 5x – 4
9a + 5
![Page 6: 3.2 Introduction to Polynomials. Identify Monomials Monomial or Term: An expression that is a constant or a product of a constant and variables that are](https://reader036.vdocuments.mx/reader036/viewer/2022062315/5697c0241a28abf838cd46fe/html5/thumbnails/6.jpg)
Identify the coefficient and degree of a
monomialTwo important parts of a monomial are its coefficient and its degree
Coefficient: The numerical factor in a monomial
Degree of a Monomial: The sum of the exponents of all the variables in the monomial
![Page 7: 3.2 Introduction to Polynomials. Identify Monomials Monomial or Term: An expression that is a constant or a product of a constant and variables that are](https://reader036.vdocuments.mx/reader036/viewer/2022062315/5697c0241a28abf838cd46fe/html5/thumbnails/7.jpg)
Example Problems
-7x2 Coefficient: -7
Degree: 2
-xy3
Coefficient: -1
Degree: 4
17Coefficient: 17
Degree: 0
![Page 8: 3.2 Introduction to Polynomials. Identify Monomials Monomial or Term: An expression that is a constant or a product of a constant and variables that are](https://reader036.vdocuments.mx/reader036/viewer/2022062315/5697c0241a28abf838cd46fe/html5/thumbnails/8.jpg)
Questions ???
![Page 9: 3.2 Introduction to Polynomials. Identify Monomials Monomial or Term: An expression that is a constant or a product of a constant and variables that are](https://reader036.vdocuments.mx/reader036/viewer/2022062315/5697c0241a28abf838cd46fe/html5/thumbnails/9.jpg)
Try Some
M6
-7x2y3
14ab
-10
![Page 10: 3.2 Introduction to Polynomials. Identify Monomials Monomial or Term: An expression that is a constant or a product of a constant and variables that are](https://reader036.vdocuments.mx/reader036/viewer/2022062315/5697c0241a28abf838cd46fe/html5/thumbnails/10.jpg)
Answers
M6
Coefficient: 1
Degree: 6
-7x2y3
Coefficient: -7
Degree: 5
14ab
Coefficient: 14
Degree: 2
-10
Coefficient: -10
Degree: 0
![Page 11: 3.2 Introduction to Polynomials. Identify Monomials Monomial or Term: An expression that is a constant or a product of a constant and variables that are](https://reader036.vdocuments.mx/reader036/viewer/2022062315/5697c0241a28abf838cd46fe/html5/thumbnails/11.jpg)
Identify like terms
Like Terms: Monomials that have the same variables raised to the same exponents.
Note: the definition does not say anything about the coefficient… just the variable and exponent…
![Page 12: 3.2 Introduction to Polynomials. Identify Monomials Monomial or Term: An expression that is a constant or a product of a constant and variables that are](https://reader036.vdocuments.mx/reader036/viewer/2022062315/5697c0241a28abf838cd46fe/html5/thumbnails/12.jpg)
Examples
5x2 and 9x2
9xyz and 5xy
7x2y and 7xy2
5a and 9A
![Page 13: 3.2 Introduction to Polynomials. Identify Monomials Monomial or Term: An expression that is a constant or a product of a constant and variables that are](https://reader036.vdocuments.mx/reader036/viewer/2022062315/5697c0241a28abf838cd46fe/html5/thumbnails/13.jpg)
Examples
YES
NO
NO
NO
5x2 and 9x2
9xyz and 5xy
7x2y and 7xy2
5a and 9A
![Page 14: 3.2 Introduction to Polynomials. Identify Monomials Monomial or Term: An expression that is a constant or a product of a constant and variables that are](https://reader036.vdocuments.mx/reader036/viewer/2022062315/5697c0241a28abf838cd46fe/html5/thumbnails/14.jpg)
You Try…-8x3 and 5x3
12mn and 12m-5y3z and y3z9t and 12T
![Page 15: 3.2 Introduction to Polynomials. Identify Monomials Monomial or Term: An expression that is a constant or a product of a constant and variables that are](https://reader036.vdocuments.mx/reader036/viewer/2022062315/5697c0241a28abf838cd46fe/html5/thumbnails/15.jpg)
![Page 16: 3.2 Introduction to Polynomials. Identify Monomials Monomial or Term: An expression that is a constant or a product of a constant and variables that are](https://reader036.vdocuments.mx/reader036/viewer/2022062315/5697c0241a28abf838cd46fe/html5/thumbnails/16.jpg)
Identify polynomials and their terms
Polynomial: A monomial or an expression that can be written as a sum of monomials
Simplest form: An expression written with the fewest symbols possible
Polynomial in one variable: A polynomial in which every variable term has the same variable
Multivariable Polynomial: A polynomial with more than one variable
![Page 17: 3.2 Introduction to Polynomials. Identify Monomials Monomial or Term: An expression that is a constant or a product of a constant and variables that are](https://reader036.vdocuments.mx/reader036/viewer/2022062315/5697c0241a28abf838cd46fe/html5/thumbnails/17.jpg)
Some Examples Please
Polynomials: 2x3 + 5x + 8
5x + 7
9x3 – 4x2 + 8x – 6
Simplest form:9x3 + (– 4x2) + 8x + (– 6)
9x3 – 4x2 + 8x – 6 Simplest Form
Both acceptable but we prefer simplest form
![Page 18: 3.2 Introduction to Polynomials. Identify Monomials Monomial or Term: An expression that is a constant or a product of a constant and variables that are](https://reader036.vdocuments.mx/reader036/viewer/2022062315/5697c0241a28abf838cd46fe/html5/thumbnails/18.jpg)
More ? .....okay
Polynomial in one variable:p3 – 5p +2
12x3 – 8x + 9
Multivariable Polynomial:
q3 + 8q3t
9px2 – 4Px2
![Page 19: 3.2 Introduction to Polynomials. Identify Monomials Monomial or Term: An expression that is a constant or a product of a constant and variables that are](https://reader036.vdocuments.mx/reader036/viewer/2022062315/5697c0241a28abf838cd46fe/html5/thumbnails/19.jpg)
Monomials are referred to as terms but polynomials are not because the often have
more than one term. In other words polynomials are made of multiple
monomials.Identify the terms in the polynomial and their coefficients:
9x3 – 4x2 + 8x – 6First Term: 9x3Coefficient: 9
Second Term: - 4x2 Coefficient: - 4
Third Term: 8xCoefficient: 8
Fourth Term: - 6 Coefficient: - 6
![Page 20: 3.2 Introduction to Polynomials. Identify Monomials Monomial or Term: An expression that is a constant or a product of a constant and variables that are](https://reader036.vdocuments.mx/reader036/viewer/2022062315/5697c0241a28abf838cd46fe/html5/thumbnails/20.jpg)
Monomial: A single-term polynomialBinomial: A polynomial with exactly two termsTrinomial: A polynomial that has exactly three terms
Polynomials that have more than three terms have no special name
![Page 21: 3.2 Introduction to Polynomials. Identify Monomials Monomial or Term: An expression that is a constant or a product of a constant and variables that are](https://reader036.vdocuments.mx/reader036/viewer/2022062315/5697c0241a28abf838cd46fe/html5/thumbnails/21.jpg)
Identify whether the polynomial is a monomial, binomial, trinomial, or has
no special name
5x3
- 3x2 + 5x
4m2 + 6m – 9
x3 + 4x2 – 9x + 2
![Page 22: 3.2 Introduction to Polynomials. Identify Monomials Monomial or Term: An expression that is a constant or a product of a constant and variables that are](https://reader036.vdocuments.mx/reader036/viewer/2022062315/5697c0241a28abf838cd46fe/html5/thumbnails/22.jpg)
Identify the degree of a polynomial
The greatest degree of any of the terms in the polynomial.
5x3 + 9x6 – 10x2 + 8x – 2Degree = 6
9x6 has the largest exponent in its term, the degree of the exponent is 6, so 6 is the degree of the polynomial.
![Page 23: 3.2 Introduction to Polynomials. Identify Monomials Monomial or Term: An expression that is a constant or a product of a constant and variables that are](https://reader036.vdocuments.mx/reader036/viewer/2022062315/5697c0241a28abf838cd46fe/html5/thumbnails/23.jpg)
Write polynomials in descending order of
degreeTo write a polynomial in descending order of degree, write the term with the greatest degree first, then the term with the next greatest degree, and so on.
5x3 + 4x2 – 3x5 – 7 + 9x
- 3x5 + 5x3 + 4x2 + 9x - 7
![Page 24: 3.2 Introduction to Polynomials. Identify Monomials Monomial or Term: An expression that is a constant or a product of a constant and variables that are](https://reader036.vdocuments.mx/reader036/viewer/2022062315/5697c0241a28abf838cd46fe/html5/thumbnails/24.jpg)
9m4 +7m9 – 3m2 + 15m – 6m7 + 2
Your turn…
![Page 25: 3.2 Introduction to Polynomials. Identify Monomials Monomial or Term: An expression that is a constant or a product of a constant and variables that are](https://reader036.vdocuments.mx/reader036/viewer/2022062315/5697c0241a28abf838cd46fe/html5/thumbnails/25.jpg)
Practice Worksheet