Pengertian Polinomial - Matematika Tingkat Lanjut Kelas XI Kurikulum Merdeka

Okay Assalamualaikum warahmatullahi

wabarakatuh good friends all

back again in the Mathematics pocket book learning video

in this video we

will discuss one material, namely

polynomials, one of the

advanced mathematics materials, yes, for

the term now for friends

who apply the independent curriculum in

their schools, yes, this is one of the

oddest business materials for

advanced mathematics grade 11, yes, first

we will discuss the meaning of

polynomials What is a polynomial or

friends may have heard

before, well, polynomials can also be

called

polynomials, yes, Why are they called polynomials

Later we will explain

so polynomials or polynomials

are an algebraic form that has a

positive integer power of more

than two Yes, both in one variable

or more, well, this is the meaning of

polynomials, so later if asked what is a polynomial,

so a polynomial, namely, it

can also be called a polynomial, yes,

namely an algebraic form that has a

positive integer power of more

than 2 Yes, it's clear, yes, for the meaning, the

highest power of a variable in

a polynomial is called the degree of

the polynomial, so this is the explanation to

distinguish one polynomial with

other polynomials, yes, it is usually

said with a polynomial of

what degree, what does that mean? For example,

there is a polynomial, later the

highest power is 5, yes, here it is said that the

power is more than 2, yes, so for example,

there is a polynomial with the

highest power, for example, 5, then it is

said to be a

polynomial of degree 5, yes, so the degree is

taken from the highest power,

once again to distinguish one polynomial

from another, it

can be understood, okay, well, in general, a

polynomial of degree n with the variable

x can be written as follows, so the

general form is more or less like this, yes, it is

almost the same as other functions

such as quadratic functions, but the note is that

this power is more than 2, so the

general form is like this, yes, AX

with a power of n plus BX with a power of n

minus 1 plus CX with a power of n

minus 2 and so on until DX

with a power of One plus e, yes, what needs to be

noted, friends, pay attention to

the power, yes, look here, the order of the

highest power is always on the left,

yes, then it must be followed by the power

after that, namely the highest power is

minus 1 then minus 2 until

the power is 1 and 0, yes, So

actually in Here there is x to the power of zero

but if x to the power of 0 is one so it is

not written so it must be in order from the

highest power to the

lowest power well more or less like this

general form of

polynomial Well for additional information

what is N, namely the power

and it must be a positive integer

then here there are ABC and D

are real numbers and are usually

called the

coefficients of the polynomial term yes

Why here there is the term term so

for example

AX ^ n this is the highest power is

said to be the first term yes the

member yes the first member then

BX to the power of n minus 1 is said to be the

second term and so on yes then the

last one which is e because there is no

variable x is said to be a

constant term yes if in quadratic functions it is

usually known as a

constant Yes but if in polynomials it is

not called a constant term Okay

so more or less like that explanation

regarding the definition and general form of

polynomials yes Well for more details

let's try to give one example question yes

After knowing the definition of

polynomials and their general form

Now we will try to analyze

which ones are

polynomials or not here there are three

examples Well the first example

2x ^ 2x ^ 2 + 4x ^ 3 - x + 1

Well, is this a polynomial or not,

so first we have to pay attention to the

order, yes, from the highest power to the

lowest power, yes, because it is a

rule, yes, to make it easier for us

to analyze a polynomial and indeed the

highest power must be on the

left, we pay attention to the question number

part A, the power is still random, right?

Let's see

which is the highest power first, which is Oh, it turns out

4x ^ 3, yes, the highest power is 3, but

it is in the second position, so we sort it

according to the order we should, the

highest power we store on the

left, meaning starting from

4x ^ 3 because the power of 3 means the

next power, what power must be reduced by

1, yes, that means after that, there must be a power of 2, is there a

power of 2 Oh, there is,

namely 2x ^ 2, meaning we write 2x ^ 2,

then next, which one is definitely x to

the power of 1, yes, here there is -x, meaning -x

and 1, okay, yes, So this is an important point

that friends must pay attention to in

compiling a polynomial, yes, whether

to determine or not to carry out

multiplication and division operations and

so on, it must be noted that it appears

the order of the powers, for example, is always the

highest power on the left

followed by the power after it Less 1

less 2 and so on Okay, after

the order is correct, then this is certainly

in accordance with the existing general form,

yes, we just need to analyze it, is it included

in the requirements as a polynomial? At

the beginning, it was explained that polynomials are

algebraic forms with

positive integer powers of more than 2, so there are

conditions, yes, one algebraic form

is said to be a polynomial here. We have a

red line as a sign, yes, which is a

condition. Well, that means no,

pay attention to the power of the x variable. Are they

all integers? Well,

here the power is 321, yes. Is it an

integer? Yes, an integer and

must be positive. Are they all positive,

positive? Yes, that means because it fulfills the

existing conditions, then this part a question

is said to be a polynomial, yes,

because all the x variables have

positive integer powers, yes, so

we sort it first according to the

existing general form, then

look at the powers, yes. Are the powers

all positive integers or not?

Yes, more than two, this is just an addition, yes,

because if the power is two,

it is still included in the category of

quadratic functions, yes, we want to discuss the

powers of more than 2. Yes, it is clear

for the a. Now we

discuss B Oh yes, there are still additional ones,

yes And remember, one polynomial with

another polynomial is usually

distinguished by looking at its power,

yes, because this has the highest power of 3,

then it is said to be a polynomial of degree

3, yes So to distinguish

one polynomial from another, it is taken

from its power Yes, it is clear, yes, it is clear

Okay, now we will discuss

the terms, meaning yes, the terms because

previously explained polynomials are

polynomials, which means Well, it was

mentioned at the beginning because this is a

polynomial, so we will discuss

the terms and their coefficients, the

first term is always the highest power

of the first term is always the

highest power here, the highest power is

already 4x ^ 3, so the

first term here we write 4x ^ 3,

then the coefficient is definitely 4, yes, the

coefficient is the value in front of

the variable x, yes, here it is 4x ^ 3,

then the coefficient is definitely 4, okay,

then the second term, the second term, because

remember here the highest power is 3,

then the second term must be a power of 2

because the power of n is minus 1, yes Is there a

power of two, there is 2x ^ 2,

then he as the second term with the

coefficient what is the

coefficient 2 okay then the

third term the third term must be what x to the

power of 1 yes because 32 must be to the power of 1 Is

there

x^1 Oh there is here that is -

remember this negative sign has a value

behind it yes means Don't let

friends later take only X

then it's wrong yes because there is a Min sign

in front of it so we take all the

third term that is

-x the coefficient what is the

coefficient approximately -1 yes okay then the

4th term which is the last one is 1 yes Well the

constant we call the term constant term

yes Well these are the terms of the

existing polynomial so it is

said to be a polynomial yes Well one more

addition friends note to be

clearer knowing How many

terms of the existing polynomial we see

from the highest power yes here the

highest power is 3 so the number of

terms must be four yes So we

add one highest number plus

one Why because there is one

constant term yes So to determine the

number of terms of the existing polynomial

just look at the highest power yes then

add 1 So that's the number of terms

as we discussed now the

highest power is 3 so we add one so it

becomes 4 yes then this polynomial

should have 4 terms Well after we analyze it

properly there are 4 terms yes first

second third and 4th can yes Okay so

friends later you have to be able to

analyze like this yes So if

there is an algebraic form friends

can analyze it Is it a

polynomial or not then it is

called a polynomial of what degree

then can also mention

the terms along with

their respective coefficients yes can we continue

now let's discuss B

pay attention to the algebraic form B

again what needs to be remembered first make sure

the polynomial is in accordance with the

existing general form yes so the

general form has been given where Well here it is

so it must be exponentiated yes the variable x

must be in exponentiated form Well we

see here x ^ 3 is appropriate yes

then followed by - x ^ 2 also Well

here there is a form

3 / x Now to make it easier for us let's change

this form to 3

1 / x yes 3 * 1 / x yes we three Save it to the

front so it's easy for us to

analyze and change it into

general form plus 4 yes Well here it is

clear yes from the question here there is

one form Here it is

1/x which is in fraction form

while the general form of the polynomial

variable x must be exponent in

the form of a natural number, right? So it

cannot be a fraction, so we have to change this 1/x

into

exponent form, how do we change it,

friends, do you still remember how?

So if you form one per X to the

power of n, yes, the fractional form we want to

change into exponent form, then

the formula is

X to the power of negative n or we

usually call it up and down, right? Well,

if the exponent is below

as the denominator, it is raised to a

negative exponent, right? So this must be

remembered. Yes, formulas like this,

friends, must be noted and must be

memorized, if possible, so that if there is

something related, there is no need to

think anymore, right, now you know it immediately spontaneously, right?

So the form of 1/x we changed

into exponent form becomes X to

the power of negative 1, right, plus 4

so that this is in accordance with the

existing general form. Now after it is in accordance with the

existing general form, we just

analyze again whether it meets the requirements

to be said to be a polynomial, namely

we look at the exponent, remember that the

polynomial must have a

positive integer. Now the

existing algebra. Well, here it turns out

there is one power of the variable x which is

negative so this is dropped yes to be

said as a polynomial so

we conclude that x to the power of 3

minus x to the power of 2 plus 3 x to the power of negative

1 + 4 is not

a polynomial yes because there is one term

that is 3x to the power of negative 1 which is

to the power of negative yes So

the powers must not be all positive so

if there is a power that is negative Then

we immediately say that it is not a

polynomial finished no need

to determine the first term the second term yes

because it is not a polynomial Yes

obviously yes So so that later if there is a

similar form of question friends

can immediately determine Oh this is

not a polynomial because there is one of the

powers that is negative yes Yes Okay

the c Come on the c Try how about the last c

Okay from the existing form x to the power of 4

minus x to the power of 3 plus 4 x to

the power of 2 plus 2 root x Is this

a polynomial or not come on what do you

think well let's see first it turns out

there is one of the terms yes There is a

root form yes the variable x has a

root form means Does this match the

existing general form yet yes

because it is not in the form exponent

means we have to change it first

How to change the root into exponent form,

how do you think So if there is a

root form x we ​​want to change into

exponent form,

what form will it be X to the power of

1/2, yes So if there is a root of x for example

Then if you want to change it into

exponent form, the formula is X to the power of 1 over

2 so that the original form of the two roots of x is

actually

2x to the power of

1/2, yes So directly we

can analyze this line Is it a

polynomial or not, how do you

think it is not, yes,

why not because there is one

term, namely 2x ^ 1/2 which has a

fractional exponent, yes, so 1/2 is a fraction, yes, if you

want to

solve it, the value is 0.5, yes, it means it is

not an integer because the requirement for a polynomial is that the

exponent must be a positive integer, namely

12345 and so on, there should be no

commas, yes, or in the form of a

division, yes 1/2 For example, so that

this c is also not a polynomial

because one of the exponents of

the variable is a fractional exponent,

so it is said that it is not a polynomial

Yes, it is clear, yes, approximately So more or less

like that to analyze

one algebraic form Is it a

polynomial or not? Remember, a

polynomial is an algebraic form that has a

positive integer power. Okay, that's

clear, okay, that's probably what

we can discuss this time regarding the

definition of a polynomial. Wait for the

next video to discuss

other materials. Stay

enthusiastic and always achieve.