[Tagalog] Write Polynomial Function into Standard Form, Determine the Degree, Leading Term, Constant
Summary
TLDRIn this educational video, the host explains how to rewrite polynomial functions into standard form and identify key components such as the degree, leading term, leading coefficient, and constant term. Using several examples, the video breaks down the steps involved, including rearranging terms, applying distributive property, and using the FOIL method. The instructor emphasizes understanding the numerical coefficient, exponent rules, and handling positive and negative constants. Viewers are encouraged to engage by liking, subscribing, and asking questions in the comments for further clarification.
Takeaways
- π The video tutorial focuses on explaining polynomial functions.
- π The presenter teaches how to rewrite polynomial functions into standard form.
- π’ The process involves identifying the degree, leading term, leading coefficient, and constant term from the standard form.
- π Example 1 demonstrates converting a simple polynomial without parentheses into standard form: x^2 - 2x + 3.
- π For Example 1, the degree is 2, the leading term is x^2, the leading coefficient is 1, and the constant term is +3.
- π Example 2 shows how to handle a polynomial with a negative leading term: -5x^3 + 4x - 6.
- π In Example 2, the degree is 3, the leading term is -5x^3, the leading coefficient is -5, and the constant term is -6.
- π The third example involves polynomial multiplication inside parentheses: x(x^2 - 7) results in x^3 - 7x.
- π For Example 3, the degree is 3, the leading term is x^3, the leading coefficient is 1, and there is no constant term (it's 0).
- π The fourth example covers the expansion of a polynomial expression: x(x + 2) - 3 simplifies to x^3 - x - 6x.
- π In Example 4, the degree is 3, the leading term is x^3, the leading coefficient is 1, and the constant term is 0.
- π’ The presenter encourages viewers to like, subscribe, and turn on notifications for more tutorials.
Q & A
What is a polynomial function?
-A polynomial function is an expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation.
How do you rewrite a polynomial into standard form?
-To rewrite a polynomial into standard form, you arrange the terms in descending order of their exponents, ensuring each term is in the form of 'coefficient * variable^exponent'.
What is the degree of a polynomial?
-The degree of a polynomial is the highest exponent of the variable present in the polynomial.
How do you find the leading term of a polynomial?
-The leading term of a polynomial is the term with the highest exponent, which is also the term that determines the polynomial's degree.
What is the leading coefficient in a polynomial?
-The leading coefficient is the numerical factor of the leading term, which is the term with the highest exponent in the polynomial.
What is the constant term in a polynomial?
-The constant term in a polynomial is the term that does not contain any variables, it is usually the term with an exponent of zero.
In the given example, what is the standard form of the polynomial 3 - 2x + x^2?
-The standard form of the polynomial 3 - 2x + x^2 is x^2 - 2x + 3.
What is the degree, leading term, leading coefficient, and constant term of the polynomial 4x - 5x^3 - 6?
-The degree of the polynomial 4x - 5x^3 - 6 is 3, the leading term is -5x^3, the leading coefficient is -5, and the constant term is -6.
How do you handle parentheses when rewriting a polynomial into standard form?
-When handling parentheses, you apply the distributive property to multiply the terms inside the parentheses by the term outside, then simplify to obtain the standard form.
In the script, what is the standard form of the polynomial x(x^2 - 7)?
-The standard form of the polynomial x(x^2 - 7) is x^3 - 7x after applying the distributive property.
What method was used to multiply the terms in the polynomial x(x + 2)(x - 3)?
-The FOIL method was used to multiply the terms in the polynomial x(x + 2)(x - 3), resulting in the standard form x^3 - x^2 - 6x.
Outlines
π Polynomial Functions Introduction
The speaker begins by welcoming viewers back to their channel and introduces the topic of polynomial functions. They explain that they will teach how to rewrite polynomial functions into standard form and how to identify the degree, leading term, leading coefficient, and constant term from the standard form. They start with an example, polynomial function number 1, which is given as 'px = 3 - 2x + x^2'. The speaker demonstrates how to write this into standard form by arranging the terms in descending order of the exponents, resulting in 'px = x^2 - 2x + 3'. They then identify the degree as 2 (the highest exponent), the leading term as 'x^2', the leading coefficient as 1 (since there is no number before 'x^2'), and the constant term as +3.
π Polynomial Functions: Degree, Terms, and Coefficients
The speaker continues with polynomial function number 2, 'f(x) = 4x - 5x^3 - 6', and explains that there are no parentheses, so the terms are written directly in standard form as 'f(x) = -5x^3 + 4x - 6'. They identify the degree as 3 (the highest exponent on the first term), the leading term as '-5x^3', and the leading coefficient as -5. The constant term is -6, which is the term without a variable. The speaker corrects a common mistake regarding the constant term, emphasizing that it should be considered as -6, not just 6, because of the negative sign. They then move on to polynomial number 3, 'y = x(x^2 - 7)', and demonstrate how to use the distributive property to expand and write it in standard form as 'y = x^3 - 7x'. They identify the degree as 3, the leading term as 'x^3', the leading coefficient as 1, and note that there is no constant term, so it is considered to be zero.
π Polynomial Functions: Expansion and Standard Form
For polynomial function number 4, the speaker shows how to expand 'x(x + 2x - 3)' using the distributive property, resulting in 'x^2 + 2x - 3x - 3'. They simplify the terms to get the standard form 'f(x) = x^2 - x - 6x'. The degree is identified as 2 (the highest exponent), the leading term as 'x^2', and the leading coefficient as 1. There is no constant term, so it is zero. The speaker concludes by thanking the viewers for watching and encourages them to comment if they have questions. They remind viewers to like and subscribe for updates and to turn on the notification bell for new video tutorials.
Mindmap
Keywords
π‘Polynomial Function
π‘Standard Form
π‘Degree
π‘Leading Term
π‘Leading Coefficient
π‘Constant Term
π‘Distributive Property
π‘Numerical Coefficient
π‘FOIL Method
π‘Parentheses in Polynomials
Highlights
Introduction to polynomial functions and explanation of key concepts like standard form, degree, leading term, leading coefficient, and constant term.
Step-by-step explanation of how to rewrite a polynomial function into its standard form.
Explanation of the degree of a polynomial, identifying it as the highest exponent in the function.
Discussion on the leading term, identified as the term with the highest exponent in the polynomial.
Clarification that the leading coefficient is the numerical coefficient of the leading term.
Explanation of the constant term as the term without a variable in the polynomial.
Worked example for the polynomial P(x) = 3 - 2x + x^2, rewriting it as x^2 - 2x + 3 and identifying the degree, leading term, leading coefficient, and constant term.
Discussion of the mistake commonly made when identifying the constant term, emphasizing that negative signs must be included.
Worked example for F(x) = 4x - 5x^3 - 6, explaining how to rearrange into standard form and identify key features like degree, leading term, and constants.
Use of parentheses to demonstrate multiplication and distribution in polynomial functions.
Explanation of the distributive property in multiplying polynomials and how to apply it step-by-step.
Worked example for y = x(x^2 - 7), showing how to distribute terms and rewrite in standard form.
Clarification that terms with no variable have a constant term of 0.
Introduction of more complex polynomial multiplication, explaining the FOIL method for expanding expressions.
Reminder to like and subscribe to the channel for more video tutorials on polynomial functions.
Transcripts
magandang buhay po at welcome po muli
dito sa aking channel ngayon naman po
ang ak pong ipapaliwanag ay about
polynomial function so given po yung
polynomial function Papaliwanag ko po sa
inyo how to rewrite into standard form
at mula po sa standard form how to get
the degree how to get the leading term
the leading coefficient and the constant
term so Ipapaliwanag ko po sa inyo step
by step
Okay so let's start mula po sa table ang
una po nating ii-f up ay ito pong
standard form at kapag nakuha po natin
yung standard form ay madali na lang
pong makuha Iyung degree leading term
leading coefficient and constant term ng
polynomial function so we will do number
1 px equ 3 - 2x + X
S itong polynomial function number 1 ay
Madali lang po natin yan na iwrite into
standard form Since wala pong
parenthesis o hindi po tayo
magmo-monitor ilalagay so magiging x s
and then followed by yung may variable
po ng exponent ay 1 kasi 2 na yung nauna
ang exponent so ito po yun so -2x po
siya kapag i-right po natin -2x din po
kukunin natin yung kanyang operation and
then yung last term natin ito 3 So pos 3
po siya kapag nilagay po natin sa dulo
since positive gawin po nating + 3 Ano
po so Yan na po ung kanyang standard
form X S - 2x +
3 Okay so balik po tayo dito sa ating
table fill up po natin yung kanyang
standard form px equ X S - 2x + 3 So
kunin po natin yung degree ang degree po
ay Yun po yung highest exponent so ang
highest exponent po diyan since X S ang
degree po ay 2 exponent ay 2 Okay next
po ay leading term ang leading term po
ay Yun po ung term na may highest
exponent So ibig sabihin ang my highest
exponent po ay x squ So yun po yung
kanyang leading term x s and then para
po sa leading coefficient ang leading
coefficient po ay Ito po yung numerical
coefficient ng leading term so ang
numerical coefficient po diyan ng
leading term ay one Since wala pong
Nakalagay ano po so one and last
Yun pong constant term ay Ito po yung
term na walang variable so Ito po plus 3
meaning to say pos 3 So paglalagay po
natin sa table Ito po ay pos 3 ang
kanyang constant
term Okay so for number two example FX
equ 4x - 5x cu - 6 So if you notice sa
atin pong function number two Ay wala p
parenthesis so wala po tayong
isi-save natin diyan ay yung may
variable pa ito po 4x so kapag ilalagay
po natin dito since positive po siya
magiging + 4x Ano po and then last ay
ito
po - 6 so wala po siyang variable Yan po
yung constant natin So lalagay lang po
natin diyan -6 so Yan na po yung ating
standard form FX e - 5x cu + 4x - 6 Okay
so fill up po natin dito sa ating table
FX equ - 5x cu + 4x - 6 ang kanyang
standard form then identify po natin
yung kanyang degree ang degree po ay
highest exponent so nasa first term Ito
po - 5x cu yung first term kaya 3 ang
kanyang degree and then yung leading
term Yun po yung may highest exponent so
Yan po yung - 5x cu Okay and then for
the leading coefficient Ito po ay
numerical coefficient po ng leading term
so ang numerical coefficient po ay -5 so
ang leading coefficient is
-5 then next ay constant term ang
constant term po ay Yun po yung term na
walang variable again so Ito po -6 po
siya kaya ang kanyang constant term ay
-6 So marami pong nagka nakamali dito
kasi ang Kinukuha lang po diyan na
constant term ay 6 Hindi po nila
iniinda ano po since - 6 basta minus po
yyan yan po ay magiging negative Okay so
for number three example y qu x * x s -
7 Okay so bago po natin ipaliwanag yung
number three click lang po muna ang like
and then subscribe kung bago ka po sa
aking channel and and notification Bell
upang sagon ay ma-update ka sa iba pang
video tutorial na aking i-upload sa mga
susunod at shoutout nga pala kay okai Ok
ox
TV Okay so for polynomial number 3 y qu
x * x s - 7 since Meron po tayong
parentheses diyan mean to say we are
going to multiply first para makuha po
natin yung kanyang standard form so to
multiply x * x s - 7 ay i-apply po na
natin yung distributive property so we
multiply first x * x s so magiging x cu
then next x Tim -7 Bakit po -7 kasi -7
so x * -7 is - 7x so Yan na po yung
product ng x * x - 7 x cu - 7x so ilagay
lang po natin yung y Yan na po yung
kanyang standard
form okay so fill up po natin sa ating
table ang kanyang standard form po ay y
equ x cu - 7x so kunin po natin yung
kanyang degree so ang degree po ay
highest exponent Ito po yung may term na
may highest exponent x cu so ang degree
po ay 3 and then leading term po ay
yyung may highest exponent so Yan din po
x
cu and then for leading
coefficient Ito po ay numerical
coefficient po ng leading term so one po
kaya ang leading coefficient ay 1 and
then for constant term Since wala pong
term diyan na walang variable so me to
say zero po ang ating constant term and
then next po ay for function number 4
Okay so ito pong function number four
natin ay
so we are going to expand i-multiply po
natin So x * x + 2 * x - 3 So ang una po
nating immuli ay x * x + 2 again if
we're going to multiply We just apply
the distributive property so first x * x
is x s and then iung second term x * 2
is 2x since plus yan kaya + 2x so Nakuha
na po natin yung product ng
unang dalawang factors so multiply po
natin diyan sa pangatlong Factor X -
3 So paano po natin i-multiply yan apply
lang po natin any method so ang apply ko
lang po diyan ay foil method ni-revise
ko po ito lang po yon X S Tim x ay x cu
para sa first term at yung last term po
natin ay
Magkabilang dulo so so 2x * -3 Bakit po
-3 kasi -3 so 2x * -3 is -
6x and then for the middle term multiply
lang po ito 2x * x is 2x s and ito X S *
-3 is
-3x S Okay since dalawa po yan na may X
S kailangan nating i-add so 2x s + - 3x
s ay - 1x s Okay so balik po tayo ang
product na po ay ito po yyung first term
po natin x cu and then yung second term
natin ay - 1x kaya - 1x s at yung
magiging last term natin ay - 6x so
magiging - 6x so Yan na po yung ating
standard form okay so balik po tayo dito
sa ating table fill up po natin yung
kanyang standard form so FX e x cu - 1x
s - 6x so ang degree po niya ay highest
exponent x cu po kaya 3 and then yyung
leading term Ian na po ang may highest
exponent ay x cu and then for the
leading coefficient numerical
coefficient po ng leading term so 1 po
ang kanyang numerical coefficient ng x
cu kaya 1 ang leading Co
okay for the constant term Wala po
tayong term diyan na walang variable
kaya zero po yung ating constant term
Okay so Salamat po sa inyong panonood
nawa po ay natulungan ko kayo sa inyong
aralin kung meron po kayong katanungan
ay comment lang po sa comment box at
hintayin po ninyo yung aking reply Be
sure lang po na kayo po ay nag-like at
nag-subscribe upang sagon Kapag Ako po
ay nag-reply ay manno po kayo sa aking
reply
Browse More Related Video
ILLUSTRATING POLYNOMIAL FUNCTIONS || GRADE 10 MATHEMATICS Q2
AP Precalculus β 1.6 End Behavior and Polynomial Functions
How to Divide Polynomials Using LONG DIVISION | Math 10
Operation on Functions/Teacher Espie
Ex1: Find an Equation of a Degree 4 Polynomial Function From the Graph of the Function
Trinomials (M2 2.3 Lesson)
5.0 / 5 (0 votes)