[Music] good day everyone so in this video lesson we will discuss about polynomial function especially how to identify the degree leading coefficient constant term of polynomial function okay what is polynomial functions anuga by a polynomial function a polynomial function is a function of the form p of x operating uh is let us p of x in polynomial function at n is equal to a sub n times x raised to n plus a sub n minus 1 times x raised to n minus 1 plus a sub n minus 2 times x raise a raise to n minus 2 plus up to a sub 1 x plus a sub 0 and this one and your a sub n is not equal to zero okay class so young last lag is uh another constant term so a big sub hand young and nothing john is a non-negative integer a sub zero and a sub one up to a sub n are real numbers so it called coefficients and then a sub n times x raised to n so ito una class is the leading term so when standard form no polynomial function at n and taught nothing gen is leading term and then a sub n naught and it's a leading term and tawagnathan is leading coefficient and then function so in this way so p of x or predicting in other notation like f of x or y so p d ring and it'll class or predict letter like for example g of x p of uh m of x so basta uh in other notation predication all right in the long p of x you might have not n so like for example melon tying p p of x is equal to two x cubed plus five x squared plus seven x minus five better nothing is nanganito f of x is equal to two x cubed plus five x squared plus seven x minus five or predicting y equals two x cubed plus five x squared plus seven x minus five so my kita you know a polynomial function okay so another 2x cubed plus 5x squared plus 7x minus 5. so that part you exponent arrange into decreasing power so he picks a b hand so thing in lageta is a variable now i am variable not indeed x so that pattern exponent arranged in decreasing orders a b sub and then constant term so mean polynomial function exponent p of x is equal to 2 x cubed plus seven x minus five okay on polynomial function so again parama sulet nathan or my right in standard form that path nothing is whole number long so that pattern negative exponent and then volume fraction x variable but nothing i want fraction exponent and radical sign and then the patrolang variables exponent in the fraction hindering our variable radical sign at well in the variable denominator nothing okay so write the given polynomial function in standard form so sabi so like for example we have f of x is equal to 4 x cubed minus 16 x minus 4 plus x to the 4 power minus x squared so panong hold it nothing uh illegal going standard form your polynomial function exponent yeah arranged in decreasing order okay arrange in decreasing order so since is some variable on the menu given uh x variable x so thinking times a variable okay plus for x cube minus x squared minus 16 x minus four so it is standard form non-polynomial function not in a given selector io another we have y is equal to one over six x to the fourth minus x squared plus five x to the fifth plus seven x cubed minus five so capacitors so that is five x to the fifth power plus one six x to the fourth power plus seven x cubed minus x squared minus 5 so into standard form 3x times x that is 3x squared 3x times 1 that is x five times x that is five x five times one that is five and then it co combination similar terms so copy three x squared three x plus five x that is eight x oh that patois equals zero eight uh of x is equal to 3x squared plus 8x plus 5. okay another example so i determine not encompolynomial function or not okay basis function for letter a okay my restriction a negative exponent of fractions exponent radical sign in variable my ah my variable was a denominator voila so therefore this is polynomial letter b so letter b is not y class time variables radical sign polynomial number three a letter c yes indirect polynomial bucket fraction exponent so not polynomial not a polynomial for letter d y is equal to 1 minus 16 x squared polynomial by an or not yes that is polynomial restriction radical sign a variable what are in denominator maritime variables are denominator you know maritime variables a denominator so hindito polynomial how about this one polynomial ba okay yeah not a polynomial parenchy okay proceed for example number i know this one so pano natin ma determinion leading term leading coefficient and the leading term latin is 2 x cube okay exponent so the answer is 2 x cubed and leading coefficient okay so again nothing leading coefficient that's a leading term and then you degree pakistan term ibis have been a constant constant or mulasian casama variable so alindito okay so example that negative five okay take notes of a sine huh negative okay i'll give you more example consider the given polynomial and fill in the table below okay halimbawayan so yeah in a factored form so standard yen so nothing standard that is f of x is equal to 2x squared plus 16x so betting and not including your leading term leading coefficient degrees exponent that is two x squared and leading coefficient that is two okay thinking that then and young degree and young pyramid as an exponent that is two and then this type is type of polynomial function quadratic so highest exponent is two and taught net engine is quadratic another f of x is equal to three x plus five times x plus one so now factored form que laguna to expand okay using foil method the answer is three x squared plus eight x plus five so capacity and leading term leading coefficient and degree so any leading term not n that is three x squared leading coefficient so the tuning nothing cocooning okay for example number three we have y is equal to 4x cubed minus 16x minus 4 plus x to the fourth minus x squared so so going out in standard form yeah so that is y is equal to x to the fourth plus four x cubed minus x squared minus sixteen x minus four so on gagorina leading term and that is x to the fourth leading coefficient one since leading coefficient is one okay y is equal to a plus four times a squared minus four eight plus sixteen okay during grade eight in the round so sum and difference okay so in expanding on let me multiply the answer is a cube plus 64 that is okay a cube plus 64. so unknown leading terminating that is a cube leading coefficient one say well so my one cn integral polynomial three so capacity and highest exponent and targeting is cubic okay number five y is equal to x squared plus x to the fourth minus three x to the sixth plus x to the fifty plus ten so indeed is in standard form okay and then coordinating leading term that is negative three x to the sixth power and then the leading coefficient is negative three and the degree of polynomial is six six in pinah matas so pagani toppak more than six now and then that indeed is uh starting okay thank you for watching this video i hope you learned something don't forget to like subscribe and hit the bell button put 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