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This module is from Elementary Algebra by Denny Burzynski and Wade Ellis, Jr.
Operations with algebraic expressions and numerical evaluations are introduced in this chapter. Coefficients are described rather than merely defined. Special binomial products have both literal and symbolic explanations and since they occur so frequently in mathematics, we have been careful to help the student remember them. In each example problem, the student is "talked" through the symbolic form.Objectives of this module: be familar with polynomials, be able classify polynomials and polynomial equations.
Overview
- Polynomials
- Classification of Polynomials
- Classification of Polynomial Equations
Polynomials
Polynomials
Let us consider the collection of all algebraic expressions that do not contain variables in the denominators of fractions and where all exponents on the variable quantities are whole numbers. Expressions in this collection are called
polynomials.
Some expressions that
are polynomials are
Some expressions that
are not polynomials are
Classification of polynomials
Polynomials can be classified using two criteria: the number of terms and degree of the polynomial.
Number of Terms |
Name |
Example |
Comment |
One |
Monomial |
|
mono means “one” in Greek. |
Two |
Binomial |
|
bi means “two” in Latin. |
Three |
Trinomial |
|
tri means “three” in Greek. |
Four or more |
Polynomial |
|
poly means “many” in Greek. |
Degree of a term containing one variable
The
degree of a term containing only
one variable is the value of the exponent of the variable. Exponents appearing on numbers do not affect the degree of the term. We consider only the exponent of the variable. For example:
8 is a monomial of degree 0. We say that a nonzero number is a term of 0 degree since it could be written as
. Since
,
. The exponent on the variable is 0 so it must be of degree 0. (By convention, the number 0 has no degree.)
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Degree of a term containing several variables
The degree of a term containing
more than one variable is the
sum of the exponents of the variables, as shown below.
Degree of a polynomial
The
degree of a polynomial is the degree of the
term of highest degree; for example:
is a trinomial of degree 3. The first term,
, is the term of the highest degree. Therefore, its degree is the degree of the polynomial.
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Questions & Answers
If auger is pair are the roots of equation x2+5x-3=0
Wayne and Dennis like to ride the bike path from Riverside Park to the beach. Dennis’s speed is seven miles per hour faster than Wayne’s speed, so it takes Wayne 2 hours to ride to the beach while it takes Dennis 1.5 hours for the ride. Find the speed of both bikers.
from theory: distance [miles] = speed [mph] × time [hours]
info #1
speed_Dennis × 1.5 = speed_Wayne × 2
=> speed_Wayne = 0.75 × speed_Dennis (i)
info #2
speed_Dennis = speed_Wayne + 7 [mph] (ii)
use (i) in (ii) => [...]
speed_Dennis = 28 mph
speed_Wayne = 21 mph
George
Let W be Wayne's speed in miles per hour and D be Dennis's speed in miles per hour. We know that W + 7 = D and W * 2 = D * 1.5.
Substituting the first equation into the second:
W * 2 = (W + 7) * 1.5
W * 2 = W * 1.5 + 7 * 1.5
0.5 * W = 7 * 1.5
W = 7 * 3 or 21
W is 21
D = W + 7
D = 21 + 7
D = 28
Salma
Devon is 32 32 years older than his son, Milan. The sum of both their ages is 54 54. Using the variables d d and m m to represent the ages of Devon and Milan, respectively, write a system of equations to describe this situation. Enter the equations below, separated by a comma.
find product (-6m+6) ( 3m²+4m-3)
what is the solution
bill
how did you arrive at this answer?
bill
i really want to learn
Amira
I only got 42 the rest i don't know how to solve it. Please i need help from anyone to help me improve my solving mathematics please
Amira
Hw did u arrive to this answer.
Aphelele
-6m(3mA²+4m-3)+6(3mA²+4m-3)
=-18m²A²-24m²+18m+18mA²+24m-18
Rearrange like items
-18m²A²-24m²+42m+18A²-18
Salma
complete the table of valuesfor each given equatio then graph.
1.x+2y=3
given that (7x-5):(2+4x)=8:7find the value of x
Nandala
please why isn't that the 0is in ten thousand place
please why is it that the 0is in the place of ten thousand
Grace
Send the example to me here and let me see
Stephen
A meditation garden is in the shape of a right triangle, with one leg 7 feet. The length of the hypotenuse is one more than the length of one of the other legs. Find the lengths of the hypotenuse and the other leg
state in which quadrant or on which axis each of the following angles given measure. in standard position would lie 89°
I am eliacin, I need your help in maths
Rood
hmm can we speak here?
Amoon
however, may I ask you some questions about Algarba?
Amoon
what the last part of the problem mean?
Roger
The Jones family took a 15 mile canoe ride down the Indian River in three hours. After lunch, the return trip back up the river took five hours. Find the rate, in mph, of the canoe in still water and the rate of the current.
Shakir works at a computer store. His weekly pay will be either a fixed amount, $925, or $500 plus 12% of his total sales. How much should his total sales be for his variable pay option to exceed the fixed amount of $925.
I'm guessing, but it's somewhere around $4335.00 I think
Lewis
12% of sales will need to exceed 925 - 500, or 425 to exceed fixed amount option. What amount of sales does that equal? 425 ÷ (12÷100) = 3541.67. So the answer is sales greater than 3541.67.
Check:
Sales = 3542
Commission 12%=425.04
Pay = 500 + 425.04 = 925.04.
925.04 > 925.00
Munster
difference between rational and irrational numbers
When traveling to Great Britain, Bethany exchanged $602 US dollars into £515 British pounds. How many pounds did she receive for each US dollar?
how to reduced echelon form
Jazmine trained for 3 hours on Saturday. She ran 8 miles and then biked 24 miles. Her biking speed is 4 mph faster than her running speed. What is her running speed?
d=r×t
the equation would be 8/r+24/r+4=3
worked out
Sheirtina
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Source:
OpenStax, Elementary algebra. OpenStax CNX. May 08, 2009 Download for free at http://cnx.org/content/col10614/1.3
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