3.2 introduction to polynomials. identify monomials monomial or term: an expression that is a...
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3.2Introduction to Polynomials
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.
Determine whether the expression is a
monomial5x
-4xy3
X6
8
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.
The following are NOT monomials
5/xy
3x2 + 5x – 4
9a + 5
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
Example Problems
-7x2 Coefficient: -7
Degree: 2
-xy3
Coefficient: -1
Degree: 4
17Coefficient: 17
Degree: 0
Questions ???
Try Some
M6
-7x2y3
14ab
-10
Answers
M6
Coefficient: 1
Degree: 6
-7x2y3
Coefficient: -7
Degree: 5
14ab
Coefficient: 14
Degree: 2
-10
Coefficient: -10
Degree: 0
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…
Examples
5x2 and 9x2
9xyz and 5xy
7x2y and 7xy2
5a and 9A
Examples
YES
NO
NO
NO
5x2 and 9x2
9xyz and 5xy
7x2y and 7xy2
5a and 9A
You Try…-8x3 and 5x3
12mn and 12m-5y3z and y3z9t and 12T
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
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
More ? .....okay
Polynomial in one variable:p3 – 5p +2
12x3 – 8x + 9
Multivariable Polynomial:
q3 + 8q3t
9px2 – 4Px2
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
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
Identify whether the polynomial is a monomial, binomial, trinomial, or has
no special name
5x3
- 3x2 + 5x
4m2 + 6m – 9
x3 + 4x2 – 9x + 2
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.
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
9m4 +7m9 – 3m2 + 15m – 6m7 + 2
Your turn…
Practice Worksheet