Polynomials

Good day students welcome to mathgotserved.com in this clip we're going to be going over

how to name polynomials or right before we get started I would some examples what were

going to do first is take a look at Om how to name polynomials using the degree of the

polynomial expression and also how to name the polynomial using the number of terms okay

so what were going to do is combine the strategy for Navy by degree and normal terms in order

to name polynomials I degree and number of terms all right let's start with the first

one which is in the mean by degree okay so if you know that the Google polynomial you

can use that information to name the polynomial so let's go over to different names that the

polynomial's have these on the degree of the polynomial of the first: we're going to be

place in the degree of the polynomial and the second column We're going to be taking

a look at what the name of the polynomial is based on the degree now what if the degree

of the polynomial is zero now before we get started with that recall that the degree is

the highest exponent of the leading term of the Om polynomial expression okay so the leading

term if the polynomial is written in standard form in this in order of degrees the term

with the highest degree that degree value is 0° of the polynomial okay so the degree

is zero the name of the polynomial is a constant in the degree is one then we have a lean year

polynomial is the degrees two we have a quadratic if you think about Om quadratic equations

the highest power exponential value is normally two okay so that's what it called quadratic

equations in the height is a Google polynomial is three then it is called the cubic think

about reason numbers to the third power what you call that is called cubed right the cube

of a number so that's why we have cubic the comes from the word cubed now how about the

fourth degree polynomial before degree polynomial is called a quartic four to okay what quartic

or or take is a how you name the fourth degree polynomial now what if you have a feet degree

polynomial if it degree polynomial is called equation take okay so for all to the to animals

P concourses these are the unique means that Om can be assigned to polynomial's bees of

your degree after that's you basically use the ordinal position of the degree to name

the polynomial so for example you have six can be called a sixth degree polynomial okay

the sixth degree polynomial advantages go on on on on like that so if you have the degree

and you call the polynomial nth degree polynomial so that basically how you name polynomials

using the degree right now what we're going to do is name the polynomial using the number

of terms okay so naming by the number of terms right so let's make of my for the chart here

to help us see how to name polynomials using the number of terms that the polynomial has

okay so will be doing after that this process is basically looking at examples in combining

naming by degree with naming by number of terms to determine the name of the polynomial

alright so in the first column we're going to take a look at the number of terms and

in the second: will going to take a look at the name of that polynomial based on the number

of terms now what if you have one term Opal in all of one term is called a multinomial

think about works that have mono associated with them so if you think about monopoly for

examples physically the financial system were one company dominates a particular sector

okay so mono you think about one if you have two terms you have even by no real think about

the Ward by means to like biweekly every two weeks or bicycle the Ms. two tires so by comes

from is associated with the word to how Monica have three terms think about bicycles right

bicycles have two tires what do the cooler three times what it holds the a cold tricycles

right so the name is going to be you might have guessed it the trinomial okay you can

also think about the geometric figure the triangle so geometric figure with three sides

rights a try would three now these are the unique names that we have for polynomial these

on the number of terms so what Om subsequent mobile terms will be named using that number

of terms okay so we have four you would you simply say the polynomial with four terms

okay and polynomial with four terms after this we don't have any unique names okay after

the third number of terms so polynomial with four terms so for an just full that pattern

you have and terms you call it the polynomial with and terms were and is an integer of course

polynomial with in terms a positive integer now let's go ahead and take a look at some

examples making use of a combination of information from these two tables that we have here now

let's try out some examples I have a chart here that's we going to be referring to distant

assist you in naming the polynomial's if you like a copy of this document to symbol equal

to mathgotserved.com on the altar to Tom this lesson is under though unique on polynomial's

so if you go to that page on boundary to you should be the to get a copy of this document's

to download for your future reference let's take a look at some examples instructions

are to name the polynomial by degree and number of terms okay so name each polynomial

by degree and number of terms polynomial number one what if we have negative

7X +2 let's determing what the number of terms are here number of terms the number of terms

Om we have one to have two terms and the degree what's the degree here now when you want to

find the degree of the polynomial you want to look for the term with the highest X exponents

the term that the variable have the highest exponent now for negative 7X the value of

the exponent for X is one okay the have the default X initial value when you do not have

any number indicate it this is a constant but it has an exponent associated with the

variable the variable is gone the reason that we do have the variable here is because of

his exponential value X to the power of zero which is one okay that's why wasn't there

so to this to term have the degree of zero in this negative 7X have the degree of one

so which is the be get out of the to the biggest degree of all the terms into degree of the

polynomial and as he can see here the highest degree is one okay so what's the name of this

polynomial we have what are two terms so let's go number of terms two terms which makes it

a binomial and we have a degree of one which makes it linear okay so what's the name the

name of this polynomial is a lean your binomial okay you start naming a Pisan the degree first

and then the number of terms second let's take a look at another example number two

what is the name of this polynomial right here negative X to the second power let's

start by determining the Om degree well is to degree first it doesn't really matter so

the degree is the highest exponent this is the only exponent that there is so by default

determine the degree of this term which is to number of terms how many terms to be have

here we have exactly one term okay so let's go back to our chart you degrees two that

is a quadratic okay and if you have one term of the monomial so how do you name this this

is a quadratic monomial so the name is a quadratic monomial let's take a look at problem number

three what if you have polynomial five right so what is the degree here to degree of a

constant is remembered there is an X to the zero given here so that tells is that the

degree is going to be zero because that's the value of the highest exponent how many

terms we have number of terms the number of terms here is just one so to go back to the

chart we have a degree of zero which Macey constant and you have one term monomial so

how do we name this the name of five is a constant monomial so that's the name of these

polynomial expression number four what if we have the polynomial expressions negative

2X plus 5X of the form +3 minus 2X to the third now let's take a look at this polynomial

let's starts with the degree what is the degree of this polynomial now want any my want to

note is that some problems minor be presented in standard form okay the terms minor be written

in descending order of degrees ask is the case here so you have to be careful to assume

that the first term of every problem determined to degree you have to take the time to inspect

the degree of every single term to determing what the biggest degree is and as he can see

the highest degree is for okay the degree of this term is one for 03 so the highest

degree is for now what is how many terms a we have here what is the number of terms as

indicated earlier we have 1234 terms now how do you name the fourth degree polynomial with

four terms as take a look at our chart you degrees for its called a quartic okay and

if you have four terms you just name the polynomial these are the number of terms you houses the

polynomial with four terms in the combined those two parts together the name of this

polynomial is equal to take this is a quartic prime or take polynomial with four terms okay

so that's how you name it let's take a look at question number five now what if you have

five minus 6X to the fifth plus X the degree of this polynomial the highest exponential

valleys five you number of terms is three so five the fifth degree polynomial is called

when take any you have three terms that's cold the trinomial so the name of this polynomial

is the Queen take trinomial okay right let's take a look at the last example for this clip

what if you have a polynomial 6X to the sixth power plus 4X square minus 5X to the third

+2 minus 4X to the fifth what is the name of this polynomial using the degree and number

of terms that start with the degree the highest exponent here is six so the can see you have

62305 to the degrees of them optically six the number of terms let's counted 12345 you

have five terms so the name of this polynomial is going to be a 6° polynomial with five

terms you notice of you have a degree greeted then five you just name it be is on the order

of the degree like 678 and any be have terms more than three just name them by the number

of two terms with four terms with 5F is in this case with six on on and on okay so this

is the name of this polynomial that we have here thanks so much for taking the time to

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