...Lesson 03.01: Review of Polynomials
Types of Expressions
Type
Definition
Example
Monomial
An expression with one term
5x
Binomial
An expression with two terms
g + 3
Trinomial
An expression with three terms
m2 + m + 1
Polynomial
An expression containing four or more terms
a5 – 3a4 – 7a3 + 2a – 1
Polynomial Arrangement
A polynomial in descending order is written with the terms arranged from largest to smallest degree.
Example: s3 – s2 + 3s – 7
A polynomial in ascending order is written with the terms arranged from smallest to largest degree.
Example: –9 + r2 + 4r4
Degree of Polynomials
The degree of a polynomial is equal to the degree of the term with the highest sum of exponents.
Example: z3 + 7z2 – 11z + 24, degree 3
Example: 5r3s – 6rs2 + q – 8, degree 4
Lesson 03.02: Polynomial Operations
Adding Polynomials
Distribute any coefficients
Combine like terms
(4x3 + 5x2 – 2x – 7) + (2x3 – 6x2 – 2)
4x3 + 5x2 – 2x – 7 + 2x3 – 6x2 – 2
6x3 – x2 – 2x – 9
Subtracting Polynomials
Distribute any coefficients – don’t forget to distribute the understood negative one!
Combine like terms
(9x2 – 7) – (8x2 + 2x + 10)
9x2 – 7 – 8x2 – 2x – 10
x2 – 2x – 17
Multiplying Polynomials
Type of Factors
Description...
...In mathematics, an algebraic expression is an expression built up from constants, variables, and a finite number of algebraic operations (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number).[1] For example, is an algebraic expression. Since taking the square root is the same as raising to the power ,
is also an algebraic expression.
A rational expression is an expression that may be rewritten to a rational fraction by using the properties of the arithmetics operations (commutative properties and associative properties of addition and multiplication, distributive property and rules for the operations on the fractions). In other words, a rational expression is an expression which may be constructed from the variables and the constants by using only the four operations of the arithmetic. Thus, is a rational expression, whereas is not.
A rational equation is an equation in which two rational fractions (or rational expressions) of the form are set equal to each other. These expressions obey the same rules as fractions. The equations can be solved by cross-multiplying. Division by zero is undefined, so that a solution causing formal division by zero is rejected.
Algebra has its own terminology to describe parts of an expression:
1 –...
...and Addition of Algebraic Expressions
Math 11
Objectives
The student should be able to:
Determine the degree of a polynomial
Identify the fundamental operations of polynomials
Definition of Terms
Algebraic expression is an expression involving constants and or variable, with all or some of the algebraic operations of addition, subtraction, division and multiplication
Definition of Terms
Components of an
Algebraic Expression
Constant term: fancy name for a number
Variable term: terms with letters
Example: 3xy – 4z + 17
Variable expression with 3 terms:
3xy, -4z, 17
2 variable terms and 1 constant term
Variable Terms
Consist of two parts
The variable(letter) part
The number part
Example:
2xy has a coefficient of 2
-6j has a coefficient of –6
W has a coefficient of 1
Definition of Terms
Monomial an algebraic expression containing only one term
ex. 4xy4
Binomial an algebraic expression containing two terms
ex. 4a + 3b
Trinomial an algebraic expression containing three terms
ex. 2a + 5b + 3c
Definition of Terms
Polynomial an algebraic expression containing two or more terms
An algebraic expression in which each term is a constant, or a constant times a positive integral power of a variable, or a constant times the product of positive...
...
Financial Polynomials
Tabitha Teasley
Math 221: Introduction to Algebra
Regina Cochran
March 22, 2014
There are many times in our life that we need to buy something big and expensive. In order to
afford or buy these item, such as cars, trucks, and houses, we need to invest or save our money over
time for that particular goal. Knowing how much money we need to begin with initially for an
investment and how much money we need to save additionally can help us to achieve that goal.
Polynomials can help you to know how much you need to start with and how much you need to save.
In this paper I will demonstrate how to use polynomials in two problems and I will simplify a
polynomialexpression, so you will know how to use this in your life to solve financial problems like
this. Because polynomials can help you achieve those monetary goal you desire.
On page 304, problem #90 states: “P dollars is invested at annual interest rate r for 1 year. If
the interest is compounded semiannually, then the polynomial P(1+r/2)^2 represents the value of
investment after 1 year “ (Dugopolski, 2012). The first part requires the polynomialexpression to be
rewritten without parenthesis. This mean FOIL or to multiply First, Outer, Inner, Last,...
...STUDIESTODAY.COM
Chapter - 2
(Polynomials)
Key Concepts
Constants : A symbol having a fixed numerical value is called a constant.
Example : 7, 3, -2, 3/7, etc. are all constants.
Variables : A symbol which may be assigned different numerical values is known as
variable.
Example :
C - circumference of circle
r - radius of circle
Where 2 &
are constants. while C and r are variable
Algebraic expressions : A combination of constants and variables. Connected by
some or all of the operations +, -, X and
Example :
is known as algebraic expression.
etc.
Terms : The several parts of an algebraic expression separated by '+' or '-' operations
are called the terms of the expression.
Example :
is an algebraic expression containing 5
terms
Polynomials : An algebraic expression in which the variables involved have only nonnegative integral powers is called a polynomial.
(i)
(ii)
is a polynomial in variable x.
is an expression but not a polynomial.
Polynomials are denoted by
Coefficients : In the polynomial
, coefficient of
respectively and we also say that +1 is the constant term in it.
Degree of a polynomial in one variable : In case of a polynomial in one variable the
highest power of the variable is called the degree of the polynomial....
...Mathematics Chapter 2: Polynomials Chapter Notes Top Definitions 1. A polynomial p(x) in one variable x is an algebraic expression in x of the form p(x) = anxn an1xn1 an 2 xn 2 ........ a2 x2 a1x a0 , where (i) a0 , a1, a2......an are constants (ii)x is a variable (iii) a0 , a1, a2......an are respectively the coefficients of xi. (iv) Each of anxn an1xn1, an 2 xn 2 ,........a2 x 2 , a1x, a0 , with an 0, is called a term of apolynomial. 2. 3. 4. The highest exponent of the variable in a polynomial is called the degree of the polynomial. A polynomial of degree one is called a linear polynomial. It is of the form ax + b. Examples: x-2, 4y+89, 3x-z. A polynomial of degree two is called a quadratic polynomial. It is of the form ax2 + bx + c. where a, b, c are real numbers and a 0 Examples: x2-2x+5, x2-3x etc. A polynomial of degree 3 is called a cubic polynomial and has the general form ax3 + bx2 + c x +d. For example: x3 2 x 2 2 x 5 etc. A real number k is said to be the zero of the polynomial p(x) if p (k) = 0.
5.
6.
Top Concepts: 1. 2. 3. 4. The graph of a polynomial p(x) of degree n can intersects or touch the x axis at atmost n points. A polynomial of degree n has at most n distinct real zeroes. The zero of the...
...POLYNOMIAL FUNCTIONS ACTIVITY
NCTM Addenda Series/Grades 9-12
The Park and Planning Commission decided to consider three factors when attempting to improve the daily profits at their sports facility:
❖ The number of all-day admission tickets sold
❖ The cost of operating the facility
❖ The price of each all-day admission ticket
After carefully analyzing their operating costs, they found that it would be impossible to cut them further.
Daily Operating Costs
Advertisements $ 55.00
Employees’ pay 310.00
Heat, lights, taxes, food, rent 435.00
Knowing that the maximum number of potential patrons is 200, the Park and Planning Commission decided to vary the price of each admission ticket to see what effect this change might have on the number of tickets sold. After much experimentation, they collected the following sales data:
Ticket Price [in $] Average Number of Tickets Sold
________________________________________________________________________
5. 158
7 142
9. 119
11 97
1. Using this information, suggest the optimal ticket price for all-day admission to the
sports facility. If you feel the need for more information, please explain why.
2. Use a graphing calculator to find the function rule of best fit for the...
...Polynomials:
Basic Operations and Factoring
Mathematics 17
Institute of Mathematics
Lecture 3
Math 17 (Inst. of Mathematics)
Polynomials: Basic Operations and Factoring
Lec 3
1 / 30
Outline
1
Algebraic Expressions and Polynomials
Addition and Subtraction of Polynomials
Multiplication of Polynomials
Division of Polynomials
2
Factoring
Sum and Difference of Two Cubes
Factoring Trinomials
Factoring By Grouping
Completing the Square
Math 17 (Inst. of Mathematics)
Polynomials: Basic Operations and Factoring
Lec 3
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Algebraic Expressions and Polynomials
An algebraic expression is any combination of variables and constants
involving a finite number of basic operations.
3x2 − 5yz 3
√
2x + 7y
Math 17 (Inst. of Mathematics)
Polynomials: Basic Operations and Factoring
Lec 3
3 / 30
Algebraic Expressions and Polynomials
An algebraic expression is any combination of variables and constants
involving a finite number of basic operations.
3x2 − 5yz 3
√
2x + 7y
A polynomial is an algebraic expression that is a sum of constants
and/or constants multiplied by variables raised to nonnegative integer
exponents.
5x3 − 2x4 y 2 + y 3
Math 17 (Inst. of Mathematics)
Polynomials: Basic Operations and Factoring
Lec 3
3 /...