Polinomial (Bagian 1) - Pengertian dan Operasi Aljabar Polinomial Matematika Peminatan Kelas XI

Hello assalamualaikum warahmatullahi

wabarakatuh meet me again with Dedy

Handayani on the math-lab channel in

this video we will learn the material of polynomials

or polynomials and this is the

first part of the video in this first part of the video

we will learn the meaning of

polynomials and algebraic operations

especially addition subtraction and

multiplication of polynomials so the material

this time is quite simple Okay

Let's just discuss the material Okay now we

will learn polynomials or polynomials the

first part we start by understanding the

meaning first so that

friends can distinguish which ones are

polynomials and which ones are not

this is the meaning of polynomials

polynomials are

algebraic forms that consist of

several terms and contain one variable with a

positive integer power the general form of a

polynomial of degree n with the variable

x can be written like this

Hi well the explanation n here This is an

integer friends these are the

highest powers this

shows the degree later so

for example the polynomial of the highest power is

5 Oh that means the polynomial is

of degree 5 and remember the power

must be a positive integer then this

part anime1 A2 to This one is

called the coefficient and its value

must be a real number and the

last part here is a

real number which is also called a constant

or fixed term. So that you can understand better,

pay attention to the following examples.

Hi 3X ^ 5 plus 2/3 x to the power of 2

minus 6x plus 7 this is a polynomial,

not clearly this is a polynomial,

the degree is five, how do we

know the degree, look at the

highest power, friends, from here this is the

highest power of 5, meaning the

polynomial is of degree

hi okay, the second example is two x to the power of 3

plus 6S squared min 2 x + 1, this is also a

polynomial and has a degree of 3, the

next example is 7 x to the power of 3 plus

6 x squared plus 3 over x plus 1

over x squared, this is a polynomial. No, this is

not a polynomial. Why because three over

x plus 1 over x squared if we

change it, yes, this is 3 Prisma one and this is

one over x to the power of 2, we use the properties of

exponents, we get something like this: 3x to

the power of negative One Plus x to the power of

negative 2 which is not and remember the

polynomial's exponent is that the exponent is whole and

positive, this is a number negative integer so

this is not a polynomial next example

5x ^ 7 plus 3 x squared plus 7 root

x this is a polynomial No this is not a

polynomial Why because this root x

if we change it to the power form is the

same

next half this is a

positive number but not an integer so it does not

meet the requirements of a polynomial okay

now we continue to the operations of

addition subtraction and multiplication of

polynomials well

this addition subtraction and multiplication of polynomials

you have learned when studying algebra in

junior high school so this is just a glimpse we just

repeat for example known PX this

polynomial 5x ^ 4 plus 3x to the power of 3

minus i5s squared plus six and

QX = 4 x ^ 3 minus 2X squared

determine the first PX plus GX

this is the addition of polynomials Then the

second PS minus X subtraction and

the third qspr you guys now how to

add subtract and

multiply two polynomials the way is

like this We start from the

Avenue section of the material first

Hi PX plus QX here the PS is

5x ^ 4 plus 3x ^ 3 minus 5 x

squared plus six this is the PS then

we add it with the like 4x ^ 3

minus 2X squared for addition

and subtraction friends operate

variables that have the same power yes here

for sman4 in the next section there is no no

enthusiasm 4 so we

just rewrite 5 SMA 4 then 3x ^ 3 is there a

power of three there is with this right 3x

^ 3 6 we add it with 4x ^ 3

then mi5x squared here there is also

a square min 2 x squared we

operate this later then the constant is 6

Now we add the coefficients

whose variables have the same power

like this for X ^ 3 we

add Najah the coefficient is 3x to the power of

3 plus 4x

three means three plus four times x to

the power of 3 like that Yes the point is add

the coefficients then this is also the same mi5s

squared minus duet this is the same

as plus min 5 minus two yes

So we get 5 Expo places plus

three places obviously 77 m03 then

plus mi5 minus 2 is minus 7 yes x to

the power of 2 plus six this is the result of

the addition and now we try

part B subtraction PX minus GX PX this one is

then subtracted Now for

subtraction be careful Don't forget to give

brackets These brackets

indicate that this subtraction

applies to every term

here yes Okay this Give brackets Now

to remove the brackets yes we

multiply mint times positive 4x ^ 3 then it

can be negative or subtraction 4x

^ 3 then this

you subtract this times here this times

here negative again negative this becomes

positive or so add 2x squared

yes Now we do the same

as before operating the

same power 5x part4 diesel there is

no more pa4 so we

rewrite then the ^ 3 3x ^ 3 here

there is mi 4x ^ 3 so like this then

the ^ 2 with the power of two again like

this and finally the constant becomes 5S

443 x to the power of 3 minus four x ^ 3

means 3 minus 4 is negative one the

coefficient becomes negative 1 x ^ 3

then mi5s squared plus 2 x

squared min 5 plus two is negative

or Min 3X ^ 2 then plus six

this is the result of the subtraction and finally

we try p x times x multiplication

Hi this is the PX polynomial then we

multiply it by the k polynomial the way

each term in PX at the point in the

PX polynomial we multiply it by QX10

5x ^ 4 we multiply it by

this k then 3x ^ 3 we

multiply it by QS too then

this part Min 5 x squared we you with

GX then 6 our constant You

also with GX so each term in PX

we multiply by

2544 this we you one by one yes

multiply by 4x ^ 3 5 * four 20

then x ^ 4 times x

cube number with the same base

if we multiply the exponents we add it

to 4 + 3 so ^ 7 then 5S

part 4 we multiply by this min 2 x

squared 5 Mint times two is Min 10 x ^ 4

times x to the power of 2 so x to the power of 16 yes

this is also the same we multiply three times

four is 12 then x ^ 3 * S ^ 3x ^ 6

then our three esma3 you guys come here

so min6x ^ 3 + 2 x ^ 5

Hi this is us You guys also mi5s squared times

4x ^ 3 so mi5 times four is min

20 x-nya ^ 2 * x ^ 3 so x ^ 5 Yamin

20s really 5 then mi5s container we

multiply by min 2 x squared min 5

times mint two is plus 10 x ^ 2 * x ^ 2x

^ 4 lastly we multiply six times

4x ^ 3 is 24 x ^ 3 6 times min 2 x

squared is mint 12 x squared lastly

we operate the same exponent yes

27 remains 20 S ^ 7 which is power-6 here

mint 10x Nam plus 12x ^ 6 Min 10

Plus 12 is positive 2 eh so positive

2xpangka 6 then min6x power-5

minus 20 x ^ 5 so min 26 s45i this

power-4 remains

and this power of three also remains and this

power of 2 remains and this is the result of the

multiplication okay

Hi Well now so that friends

understand better we will try to work on some of the

following example questions Okay we start

from the first example question the

following algebraic form which is a

polynomial is Come on, which one is

included in the minimum we start from the

option Oh you let's try it 1/3 x to the power of

6 minus 2x to the power of 3 minus a quarter

plus x + 7 polynomial conditions

Hi the power is a

positive integer then the coefficient is real and

the constant is real like that right Well

here there is nothing that violates

the rules right Tan phi per 4 this value

sells spare parts is 45° tan45 degrees

is one so this value is 1

obviously then xp2 is the same

as half X means the coefficient

is half the prayer the coefficient is

real this is included in the Kernel so this is a

polynomial we try the b x ^ 5

minus 3 x squared plus two per x

plus 7 6 parts here two perex is the

same as 2x to the power of negative one the

power is negative the polynomial the

power must be whole and positive so

this is not a polynomial now the c 3x

^ 5 minus x squared plus 2 years

x plus one this is not a polynomial

because the variable x is

Edi trigonometry here yes then

the d3s to the power of 3 minus x squared

cos phi this costing is no problem

friends because the value is clear

but the problem here two

per x squared is the same as 2x to

the power of negative 2 the power is negative

so this is also not a polynomial and the

last one is also not a polynomial

the variable is in trigonometry Okay so

the answer to this question is a we

discuss question number 2 the degree of the polynomial ia 6x to the

power of 3 min 2 x squared min 1 is

remember the degree is the

highest power yes here the highest power is

clearly three so the degree is

three easy Let's move on to the

third example, the third example of the coefficient of x

squared in the polynomial 5x ^ 4, if the

Indonesian spelling is used, yes,

polynomial 5 SP4 Min 4x

3 plus 3 x squared min 2 x + 1

is the coefficient of X squared DX

squared, this one, friends,

this coefficient is three, so

the answer is C if the polynomial PX has a

degree of 4 and the polynomial QX

has a degree of 6°, the polynomial resulting from the

subtraction of PX minus x is Well,

for addition and subtraction when the

polynomials have different degrees, take the

largest degree, the result will be = the

highest degree, for example, this is PX with a degree of 4

and QX with a degree of Nam, then the result of

the subtraction, both cxmine QX and

kmine PX, will be = the highest degree,

friends, so the result will be = the

highest degree, which is six, but when

the degree is the same PX with GX,

for example, this is the degree of this place, degree

4, if subtracted or added

Hi, then the result will be equal to

four again or it can be smaller, Well, it

depends on the coefficient, okay, let's move on to the

next example, it is known that PS = 3x ^ 3

minus 6 x squared plus 12 x

plus 3 and QX = 2x ^ 4 Min 3x ^ 3 +

2 x squared min 6 the result of the sum of PX

plus GX remember that the sum we

operate on the same power here the

highest power is the power-4

so PX plus KSA is the same as this

power-4 in PS is reluctant to exist So we

just write Bang 2x power

Hi plus now the third power is

3x ^ 3 we add with this Min

3x ^ 3 3x ^ 3 plus min 3x ^ 3

stop zero right finished yes become zero

then ^ 2

Hi min6x squared plus 2x squared

will be Min 4 x squared

Hi Min 4 x squared then this x variable

12x here does not exist So we

rewrite 12x now the constant is 3

plus min 6 is min 3 now this is

the result 2x power 4 Min 4 x squared

plus 12 x min 3 the answer is B yes

okay the next is known FX = 3 X ^

4 minus x to the power of 3 minus x

plus 1 and GX = x to the power of 3 min 5 x

squared min 4x + 8 the result of subtraction FX

minus GX

Hi, we subtract yes

Hi FX minus GX the effect we write 3

X ^ 4 minus x to the power of 3 minus x

plus one minus GX Now for

subtraction Don't forget to put parentheses

Hi, this is x to the power of 3 min 5 x squared

minus 4x plus 8 and now

we open the parentheses this is still min x to

the power of 3 min x + 1 and now we

open the parentheses negative positive

so negative x ^ 3 negative times negative

this becomes + 5 x squared negative times

negative so please 4x negative times

positive becomes min 8 Now we

operate the same exponent for x

^ 4 This is no longer there So we

just rewrite the exponent 3 min x to

the power of 3 minus x to the power of 3 becomes min

two x to the power of 3

a ^ 2 is from here plus 5x ^ 2 the

other ^ is min x plus 4x becomes plus 3x

then the constant is One Plus

negative 8 negative 7 yes Well this is the result

3x to the power of 4 minus two x to the power of 3

then + 5 x squared plus three x

minus 7 this one yes the answer is

let's continue the next example if the

polynomial PX has a degree of 5 and the

polynomial PX has a degree of 3 then the degree of the polynomial is the

result of multiplying PX times X

Well for the result of the multiplication of the degrees it

will be the same as the sum of the two degrees of the

polynomial remember if

multiplied the powers are added together means

this is five we add with three

the result is 8B

Hi next question The degree of the polynomial 3

x squared minus x to the power of 3 multiply by

2 x ^ 3 + 6 x + 1 is the degree it

is the highest power so let's just look at the

power friends x squared

raised to the power of three numbers to the power

if raised again the power is multiplied by

n this will be x to the power of 6

then later it will be multiplied by this

2x to the power of 3 if multiplied

the powers are added together it will be

x ^ 9 so the answer is B

the degree is 9 Okay up to here First,

the discussion of polynomials, part one, until

we meet again in the next video. Alaikum

warohmatullohi wabarokatuh, hello, hello, hello, hello