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  • 00:01

    - WELCOME TO AN INTRODUCTION TO POLYNOMIALS.
    - WELCOME TO AN INTRODUCTION TO POLYNOMIALS.

  • 00:03

    THE GOAL OF THIS VIDEO IS TO IDENTIFY POLYNOMIALS
    THE GOAL OF THIS VIDEO IS TO IDENTIFY POLYNOMIALS

  • 00:06

    AND KNOW THE DIFFERENT VOCABULARY TERMS USED
    AND KNOW THE DIFFERENT VOCABULARY TERMS USED

  • 00:09

    WHEN DISCUSSING POLYNOMIALS.
    WHEN DISCUSSING POLYNOMIALS.

  • 00:11

    SO, LET'S START OFF WITH SOME VOCABULARY.
    SO, LET'S START OFF WITH SOME VOCABULARY.

  • 00:13

    A TERM CAN BE A NUMBER, A VARIABLE, A PRODUCT OF NUMBERS
    A TERM CAN BE A NUMBER, A VARIABLE, A PRODUCT OF NUMBERS

  • 00:17

    AND/OR VARIABLES, OR A QUOTIENT OF NUMBERS AND/OR VARIABLES.
    AND/OR VARIABLES, OR A QUOTIENT OF NUMBERS AND/OR VARIABLES.

  • 00:21

    HERE ARE SOME EXAMPLES OF SOME TERMS,
    HERE ARE SOME EXAMPLES OF SOME TERMS,

  • 00:24

    5X, NEGATIVE 3A SQUARED, B CUBED, 1/5,
    5X, NEGATIVE 3A SQUARED, B CUBED, 1/5,

  • 00:30

    NEGATIVE 8 OVER X SQUARED, M OVER N,
    NEGATIVE 8 OVER X SQUARED, M OVER N,

  • 00:35

    7X TO THE POWER OF NEGATIVE 3.
    7X TO THE POWER OF NEGATIVE 3.

  • 00:37

    THESE ARE ALL TERMS BECAUSE THEY SATISFY THESE CONDITIONS.
    THESE ARE ALL TERMS BECAUSE THEY SATISFY THESE CONDITIONS.

  • 00:40

    NOW, MONOMIAL IS A REAL NUMBER AND/OR THE PRODUCT OF VARIABLES
    NOW, MONOMIAL IS A REAL NUMBER AND/OR THE PRODUCT OF VARIABLES

  • 00:44

    WITH NON-NEGATIVE EXPONENTS.
    WITH NON-NEGATIVE EXPONENTS.

  • 00:47

    SO, SOME OF THESE TERMS ARE MONOMIALS
    SO, SOME OF THESE TERMS ARE MONOMIALS

  • 00:49

    AND SOME OF THEM AREN'T, 5X, NEGATIVE 3A SQUARED, B CUBED
    AND SOME OF THEM AREN'T, 5X, NEGATIVE 3A SQUARED, B CUBED

  • 00:56

    AND 1/5 ARE THE ONLY TERMS THAT ARE ALSO MONOMIALS.
    AND 1/5 ARE THE ONLY TERMS THAT ARE ALSO MONOMIALS.

  • 01:02

    THESE THREE TERMS ARE NOT MONOMIALS
    THESE THREE TERMS ARE NOT MONOMIALS

  • 01:04

    BECAUSE THESE TWO INVOLVE QUOTIENTS OF VARIABLES
    BECAUSE THESE TWO INVOLVE QUOTIENTS OF VARIABLES

  • 01:08

    AND THIS ONE HAS A NEGATIVE EXPONENT.
    AND THIS ONE HAS A NEGATIVE EXPONENT.

  • 01:11

    A POLYNOMIAL IS A MONOMIAL OR A SUM OF MONOMIALS.
    A POLYNOMIAL IS A MONOMIAL OR A SUM OF MONOMIALS.

  • 01:15

    REMEMBER THAT SUBTRACTION CAN BE REWRITTEN AS ADDITION,
    REMEMBER THAT SUBTRACTION CAN BE REWRITTEN AS ADDITION,

  • 01:18

    SO IT MAY SHOW UP AS A SUBTRACTION OR MONOMIALS.
    SO IT MAY SHOW UP AS A SUBTRACTION OR MONOMIALS.

  • 01:22

    SO, FOR EXAMPLE, 5X + 3 IS A POLYNOMIAL.
    SO, FOR EXAMPLE, 5X + 3 IS A POLYNOMIAL.

  • 01:27

    -X CUBED + 5Y SQUARED - 8 IS ALSO A POLYNOMIAL.
    -X CUBED + 5Y SQUARED - 8 IS ALSO A POLYNOMIAL.

  • 01:34

    NOW, POLYNOMIALS DO HAVE FURTHER CLASSIFICATION
    NOW, POLYNOMIALS DO HAVE FURTHER CLASSIFICATION

  • 01:37

    BASED UPON THE NUMBER OF TERMS IN THE EXPRESSION.
    BASED UPON THE NUMBER OF TERMS IN THE EXPRESSION.

  • 01:39

    SO FOR EXAMPLE, IF WE HAVE MONOMIALS,
    SO FOR EXAMPLE, IF WE HAVE MONOMIALS,

  • 01:43

    MONO MEANS 1 SO WE HAVE THE 1 TERM.
    MONO MEANS 1 SO WE HAVE THE 1 TERM.

  • 01:45

    ALL OF THESE ARE MONOMIALS.
    ALL OF THESE ARE MONOMIALS.

  • 01:47

    BINOMIALS CONSIST OF TWO MONOMIALS
    BINOMIALS CONSIST OF TWO MONOMIALS

  • 01:49

    CONNECTED WITH ADDITION OR SUBTRACTION.
    CONNECTED WITH ADDITION OR SUBTRACTION.

  • 01:52

    HERE ARE SOME EXAMPLES OF BINOMIALS.
    HERE ARE SOME EXAMPLES OF BINOMIALS.

  • 01:54

    IF THE POLYNOMIAL HAS 3 TERMS, IT'S CALLED A TRINOMIAL.
    IF THE POLYNOMIAL HAS 3 TERMS, IT'S CALLED A TRINOMIAL.

  • 02:00

    HERE ARE TWO EXAMPLE OF TRINOMIALS
    HERE ARE TWO EXAMPLE OF TRINOMIALS

  • 02:03

    AND ONCE A POLYNOMIAL GETS PAST THREE TERMS,
    AND ONCE A POLYNOMIAL GETS PAST THREE TERMS,

  • 02:05

    WE USUALLY JUST CALL IT A POLYNOMIAL.
    WE USUALLY JUST CALL IT A POLYNOMIAL.

  • 02:07

    THE WORD POLY MEANS MANY.
    THE WORD POLY MEANS MANY.

  • 02:11

    LET'S GO AHEAD AND CONSIDER THIS POLYNOMIAL.
    LET'S GO AHEAD AND CONSIDER THIS POLYNOMIAL.

  • 02:14

    THE FIRST THING WE SHOULD BE ABLE TO DO
    THE FIRST THING WE SHOULD BE ABLE TO DO

  • 02:15

    IS LIST THE TERMS OF THE POLYNOMIAL
    IS LIST THE TERMS OF THE POLYNOMIAL

  • 02:18

    AND THE ONLY THING YOU HAVE TO BE CAREFUL ABOUT
    AND THE ONLY THING YOU HAVE TO BE CAREFUL ABOUT

  • 02:19

    IS DEALING WITH THE SUBTRACTION.
    IS DEALING WITH THE SUBTRACTION.

  • 02:21

    SO, THE FIRST TERM WOULD BE 4X SQUARED, Y CUBED.
    SO, THE FIRST TERM WOULD BE 4X SQUARED, Y CUBED.

  • 02:26

    THE SECOND TERM--REMEMBER THE ORIGINAL DEFINITION
    THE SECOND TERM--REMEMBER THE ORIGINAL DEFINITION

  • 02:28

    OF A POLYNOMIAL WAS THE SUM OF MONOMIALS.
    OF A POLYNOMIAL WAS THE SUM OF MONOMIALS.

  • 02:32

    SO, THIS IS THE SAME AS PLUS A NEGATIVE 12X CUBED.
    SO, THIS IS THE SAME AS PLUS A NEGATIVE 12X CUBED.

  • 02:36

    SO, THE TERM IS NEGATIVE 12X CUBED.
    SO, THE TERM IS NEGATIVE 12X CUBED.

  • 02:40

    I JUST THINK THAT YOU TAKE THE SIGN WITH IT.
    I JUST THINK THAT YOU TAKE THE SIGN WITH IT.

  • 02:42

    IF IT'S A MINUS SIGN, SHOOT IT AS A NEGATIVE.
    IF IT'S A MINUS SIGN, SHOOT IT AS A NEGATIVE.

  • 02:45

    THE THIRD TERM WOULD BE 24XY.
    THE THIRD TERM WOULD BE 24XY.

  • 02:48

    FOURTH TERM WOULD BE X AND THE FIFTH TERM AGAIN
    FOURTH TERM WOULD BE X AND THE FIFTH TERM AGAIN

  • 02:52

    WOULD BE A NEGATIVE 15.
    WOULD BE A NEGATIVE 15.

  • 02:54

    NEXT, WE WANT TO TALK ABOUT DEGREE.
    NEXT, WE WANT TO TALK ABOUT DEGREE.

  • 02:56

    THE DEGREE OF A TERM IS THE NUMBER OF VARIABLE FACTORS
    THE DEGREE OF A TERM IS THE NUMBER OF VARIABLE FACTORS

  • 02:59

    IN THAT TERM.
    IN THAT TERM.

  • 03:01

    YOU CAN ALSO SAY THE DEGREE OF A TERM
    YOU CAN ALSO SAY THE DEGREE OF A TERM

  • 03:04

    IS THE SUM OF THE EXPONENTS ON THE VARIABLES.
    IS THE SUM OF THE EXPONENTS ON THE VARIABLES.

  • 03:07

    SO, THE DEGREE OF THIS FIRST TERM,
    SO, THE DEGREE OF THIS FIRST TERM,

  • 03:10

    BECAUSE THERE'S TWO FACTORS OF X HERE AND THREE FACTORS OF Y,
    BECAUSE THERE'S TWO FACTORS OF X HERE AND THREE FACTORS OF Y,

  • 03:14

    THE DEGREE OF THIS TERM WOULD BE 5.
    THE DEGREE OF THIS TERM WOULD BE 5.

  • 03:17

    YOU CAN SEE AN EASY WAY TO DO THAT
    YOU CAN SEE AN EASY WAY TO DO THAT

  • 03:18

    IS JUST ADD THE POWERS ON THE VARIABLES.
    IS JUST ADD THE POWERS ON THE VARIABLES.

  • 03:21

    THIS TERM HAS DEGREE 3.
    THIS TERM HAS DEGREE 3.

  • 03:25

    THIS TERM HAS ONE FACTOR OF X, ONE FACTOR OF Y,
    THIS TERM HAS ONE FACTOR OF X, ONE FACTOR OF Y,

  • 03:29

    THEREFORE, THE TERM HAS DEGREE TWO.
    THEREFORE, THE TERM HAS DEGREE TWO.

  • 03:32

    THIS WOULD BE X TO THE FIRST, SO IT'S A DEGREE ONE TERM.
    THIS WOULD BE X TO THE FIRST, SO IT'S A DEGREE ONE TERM.

  • 03:36

    THIS DOES NOT HAVE ANY FACTORS OF A VARIABLE,
    THIS DOES NOT HAVE ANY FACTORS OF A VARIABLE,

  • 03:39

    THEREFORE THE DEGREE IS ZERO.
    THEREFORE THE DEGREE IS ZERO.

  • 03:41

    OR YOU COULD ALSO THINK OF IF YOU HAD TO INCLUDE A VARIABLE,
    OR YOU COULD ALSO THINK OF IF YOU HAD TO INCLUDE A VARIABLE,

  • 03:45

    IT WOULD HAVE TO BE SOMETHING LIKE X TO THE ZERO POWER
    IT WOULD HAVE TO BE SOMETHING LIKE X TO THE ZERO POWER

  • 03:48

    BECAUSE THAT WOULD BE EQUAL TO ONE,
    BECAUSE THAT WOULD BE EQUAL TO ONE,

  • 03:50

    WHICH WOULD NOT CHANGE THE TERM.
    WHICH WOULD NOT CHANGE THE TERM.

  • 03:52

    THE LEADING TERM OF A POLYNOMIAL
    THE LEADING TERM OF A POLYNOMIAL

  • 03:54

    IS THE TERM OF THE HIGHEST DEGREE.
    IS THE TERM OF THE HIGHEST DEGREE.

  • 03:56

    SO, THIS TERM IN THE POLYNOMIAL HAS DEGREE 5,
    SO, THIS TERM IN THE POLYNOMIAL HAS DEGREE 5,

  • 04:00

    THEREFORE WE CALL IT THE LEADING TERM.
    THEREFORE WE CALL IT THE LEADING TERM.

  • 04:04

    NOTICE THE TERMS ARE IN ORDER
    NOTICE THE TERMS ARE IN ORDER

  • 04:05

    FROM HIGHEST DEGREE TO LOWEST DEGREE
    FROM HIGHEST DEGREE TO LOWEST DEGREE

  • 04:09

    AND THIS IS CALLED DESCENDING ORDER.
    AND THIS IS CALLED DESCENDING ORDER.

  • 04:12

    CONSIDERING THE SAME POLYNOMIAL,
    CONSIDERING THE SAME POLYNOMIAL,

  • 04:14

    THE DEGREE OF A POLYNOMIAL
    THE DEGREE OF A POLYNOMIAL

  • 04:16

    IS THE SAME AS THE DEGREE OF THE LEADING TERM.
    IS THE SAME AS THE DEGREE OF THE LEADING TERM.

  • 04:20

    REMEMBER, THIS IS THE LEADING TERM.
    REMEMBER, THIS IS THE LEADING TERM.

  • 04:22

    IT HAD DEGREE 5, THEREFORE THE DEGREE OF THE ENTIRE POLYNOMIAL
    IT HAD DEGREE 5, THEREFORE THE DEGREE OF THE ENTIRE POLYNOMIAL

  • 04:26

    IS DEGREE 5.
    IS DEGREE 5.

  • 04:29

    NEXT, THE COEFFICIENT OF A TERM
    NEXT, THE COEFFICIENT OF A TERM

  • 04:31

    IS THE CONSTANT FACTOR OF THE NUMBER PART OF THE TERM.
    IS THE CONSTANT FACTOR OF THE NUMBER PART OF THE TERM.

  • 04:35

    SO, THE COEFFICIENT OF THIS LEADING TERM WOULD BE 4
    SO, THE COEFFICIENT OF THIS LEADING TERM WOULD BE 4

  • 04:39

    THE COEFFICIENT OF THE SECOND TERM WOULD BE -12.
    THE COEFFICIENT OF THE SECOND TERM WOULD BE -12.

  • 04:43

    THE COEFFICIENT WOULD BE 24 FOR THIS TERM.
    THE COEFFICIENT WOULD BE 24 FOR THIS TERM.

  • 04:47

    THIS COEFFICIENT WOULD BE 1
    THIS COEFFICIENT WOULD BE 1

  • 04:50

    AND THIS COEFFICIENT WOULD BE NEGATIVE 15.
    AND THIS COEFFICIENT WOULD BE NEGATIVE 15.

  • 04:54

    THE LEADING COEFFICIENT IS THE COEFFICIENT OF THE LEADING TERM
    THE LEADING COEFFICIENT IS THE COEFFICIENT OF THE LEADING TERM

  • 04:57

    SO IN THIS CASE--
    SO IN THIS CASE--

  • 04:58

    THEREFORE IN THIS CASE, THE LEADING COEFFICIENT IS 4.
    THEREFORE IN THIS CASE, THE LEADING COEFFICIENT IS 4.

  • 05:01

    OKAY, LET'S SEE IF WE CAN PUT ALL THESE PIECES TOGETHER.
    OKAY, LET'S SEE IF WE CAN PUT ALL THESE PIECES TOGETHER.

  • 05:04

    WE'RE GIVEN A POLYNOMIAL.
    WE'RE GIVEN A POLYNOMIAL.

  • 05:06

    WE WANT TO FIRST LIST THE TERMS,
    WE WANT TO FIRST LIST THE TERMS,

  • 05:08

    2A CUBED, B SQUARED IS THAT FIRST TERM,
    2A CUBED, B SQUARED IS THAT FIRST TERM,

  • 05:11

    7A SQUARED, B SQUARED IS OUR SECOND TERM.
    7A SQUARED, B SQUARED IS OUR SECOND TERM.

  • 05:15

    OUR THIRD TERM IS NEGATIVE 0.5AB SQUARED.
    OUR THIRD TERM IS NEGATIVE 0.5AB SQUARED.

  • 05:20

    THE FOURTH TERM IS 25B AND THE FIFTH TERM IS A -21.
    THE FOURTH TERM IS 25B AND THE FIFTH TERM IS A -21.

  • 05:25

    REMEMBER THE COEFFICIENTS ARE THE CONSTANT FACTORS
    REMEMBER THE COEFFICIENTS ARE THE CONSTANT FACTORS

  • 05:28

    OF THE TERM OR THE NUMBER PART.
    OF THE TERM OR THE NUMBER PART.

  • 05:30

    SO, THIS COEFFICIENT IS 2.
    SO, THIS COEFFICIENT IS 2.

  • 05:32

    THIS COEFFICIENT IS 7.
    THIS COEFFICIENT IS 7.

  • 05:34

    THIS COEFFICIENT IS NEGATIVE 0.5, 25, AND NEGATIVE 21.
    THIS COEFFICIENT IS NEGATIVE 0.5, 25, AND NEGATIVE 21.

  • 05:41

    NEXT, THE DEGREE OF EACH TERM
    NEXT, THE DEGREE OF EACH TERM

  • 05:43

    IS THE NUMBER OF VARIABLE FACTORS
    IS THE NUMBER OF VARIABLE FACTORS

  • 05:45

    OR THE SUM OF THE EXPONENTS ON THE VARIABLES.
    OR THE SUM OF THE EXPONENTS ON THE VARIABLES.

  • 05:48

    SO, THIS TERM HAS DEGREE 5.
    SO, THIS TERM HAS DEGREE 5.

  • 05:51

    THIS TERM HAS DEGREE 4.
    THIS TERM HAS DEGREE 4.

  • 05:54

    THIS TERM HAS DEGREE 3,
    THIS TERM HAS DEGREE 3,

  • 05:56

    TWO FACTORS OF B AND ONE FACTOR OF A.
    TWO FACTORS OF B AND ONE FACTOR OF A.

  • 05:59

    THIS HAS ONE FACTOR OF B.
    THIS HAS ONE FACTOR OF B.

  • 06:02

    THIS HAS ZERO VARIABLE FACTORS, SO IT'S DEGREE ZERO.
    THIS HAS ZERO VARIABLE FACTORS, SO IT'S DEGREE ZERO.

  • 06:06

    THE LEADING TERM IN THIS CASE,
    THE LEADING TERM IN THIS CASE,

  • 06:07

    BECAUSE IT IS IN DESCENDING ORDER, WOULD BE THE FIRST TERM.
    BECAUSE IT IS IN DESCENDING ORDER, WOULD BE THE FIRST TERM.

  • 06:10

    THAT'S NOT ALWAYS THE CASE,
    THAT'S NOT ALWAYS THE CASE,

  • 06:12

    SO YOU WANT TO MAKE SURE YOU CHECK TO CHOOSE THE TERM
    SO YOU WANT TO MAKE SURE YOU CHECK TO CHOOSE THE TERM

  • 06:15

    WITH THE HIGHEST DEGREE.
    WITH THE HIGHEST DEGREE.

  • 06:18

    THE LEADING COEFFICIENT THEN OF COURSE IS 2
    THE LEADING COEFFICIENT THEN OF COURSE IS 2

  • 06:21

    AND THE DEGREE OF THE POLYNOMIAL
    AND THE DEGREE OF THE POLYNOMIAL

  • 06:23

    IS THE SAME AS THE DEGREE OF THE LEADING TERM, WHICH IS 5.
    IS THE SAME AS THE DEGREE OF THE LEADING TERM, WHICH IS 5.

  • 06:29

    HOPEFULLY, ALL OF THIS NEW VOCABULARY MAKES SENSE
    HOPEFULLY, ALL OF THIS NEW VOCABULARY MAKES SENSE

  • 06:31

    AND YOU FOUND THIS VIDEO HELPFUL.
    AND YOU FOUND THIS VIDEO HELPFUL.

  • 06:33

    THANK YOU AND HAVE A GOOD DAY.
    THANK YOU AND HAVE A GOOD DAY.

All noun
introduction
/ˌintrəˈdəkSH(ə)n/
word
bringing of something into use for first time

Introduction to Polynomials

156,698 views

Mathispower4u

Video Language:

  • English

Caption Language:

  • English (en)

Accent:

  • English

Speech Time:

98%
  • 6:33 / 6:40

Speech Rate:

  • 163 wpm - Fast

Category:

  • Education

Tags :

Intro:

- WELCOME TO AN INTRODUCTION TO POLYNOMIALS.. THE GOAL OF THIS VIDEO IS TO IDENTIFY POLYNOMIALS. AND KNOW THE DIFFERENT VOCABULARY TERMS USED. WHEN DISCUSSING POLYNOMIALS.. SO, LET'S START OFF WITH SOME VOCABULARY.. A TERM CAN BE A NUMBER, A VARIABLE, A PRODUCT OF NUMBERS
AND/OR VARIABLES, OR A QUOTIENT OF NUMBERS AND/OR VARIABLES.
HERE ARE SOME EXAMPLES OF SOME TERMS,. 5X, NEGATIVE 3A SQUARED, B CUBED, 1/5,. NEGATIVE 8 OVER X SQUARED, M OVER N,. 7X TO THE POWER OF NEGATIVE 3.. THESE ARE ALL TERMS BECAUSE THEY SATISFY THESE CONDITIONS.
NOW, MONOMIAL IS A REAL NUMBER AND/OR THE PRODUCT OF VARIABLES
WITH NON-NEGATIVE EXPONENTS.. SO, SOME OF THESE TERMS ARE MONOMIALS. AND SOME OF THEM AREN'T, 5X, NEGATIVE 3A SQUARED, B CUBED
AND 1/5 ARE THE ONLY TERMS THAT ARE ALSO MONOMIALS.
THESE THREE TERMS ARE NOT MONOMIALS. BECAUSE THESE TWO INVOLVE QUOTIENTS OF VARIABLES. AND THIS ONE HAS A NEGATIVE EXPONENT..

Video Vocabulary

squared

/skwerd/

adjective verb

(Of number) multiplied by itself (e.g. 2 x 2). To straighten the edge to form a four-sided shape.

vocabulary

/vōˈkabyəˌlerē/

noun

body of words used in particular language.

introduction

/ˌintrəˈdəkSH(ə)n/

noun

Opening part of a text or piece of music.

remember

/rəˈmembər/

verb

To hold a thought in your mind to not forget it.

monomial

/məˈnōmēəl/

adjective noun other

(of algebraic expression) consisting of one term. algebraic expression consisting of one term. .

involve

/inˈvälv/

verb

include as necessary or integral part.

negative

/ˈneɡədiv/

adjective exclamation noun verb

Focusing on the bad aspects; pessimistic. no. Image on camera film used to make a photo. refuse to accept.

subtraction

/səbˈtrakSH(ə)n/

noun

Act of taking one value away from another.

examples

/iɡˈzampəl/

noun other verb

thing characteristic of its kind. Things, people, which represent a category. be illustrated or exemplified.

polynomial

/ˌpäləˈnōmēəl/

adjective noun

Having the character of a polynomial. expression of more than two algebraic terms.

discussing

/dəˈskəs/

verb

To talk about seriously or in great detail.

rewritten
verb

To write again to improve, or correct errors.

quotient

/ˈkwōSHənt/

noun

result obtained by dividing one quantity by another.

welcome - welcome

/ˈwelkəm/

adjective exclamation noun verb

Being what was wanted or needed. used to greet someone in polite or friendly way. Friendly greeting to someone who has arrived. greet someone arriving in polite or friendly way.

numbers

/ˈnəmbər/

noun other verb

arithmetical value expressed by word, symbol, or figure. Symbols such as 1, 2, 56, 793. To put numbers on things.