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4.1 Day 1 - Polynomials ALGEBRA 2

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this lesson is polynomials 4.1 lesson 1 what are polynomial functions so what is a monomial do you remember from Algebra 1 it is a number a variable or the product early number and one or more variables examples probably think of them we're doing this lesson so that you can practice Dallas online examples would be 5 x 5 x squared and what's the negative in there those are monomials of 5 is just a number the x is a variable and the negative 5x squared is a product of a number and one or more variables next question is what is a paw remember poly means what so many monomials and you can causes at any time and if you need to think about something a little bit more or write down the information a little slower is a monomial or the sum at two or more monomials and examples what do Negative X + 2 x - 3 and you can write this as a sign negative x squared plus 2X plus negative 3x just remember that. this right here cuz you would that you can write that as adding the opposite so it is still some even though it looks like a a subtraction sign you can rewrite it as a sum what is the term of a polynomial so looking back up that example their negative x squared plus 2X minus 3 the terms would be negative x squared 2X and then negative 3 so it turn what is a monomial the polynomial and what are the terms separated by they're separated by classes Candice example down here can be Rewritten as 5 x 1/4 + -3x + 2x + -8 so when you see subtraction again remember that subtraction is the same as I in opposite I'm so it can be written as the sum attraction is adding opposite so just kind of remember that that might help you figure out the terms so let's just pick a couple of terms here return number one Western number one Alex and 4th what is term number 2 take a sign with it 3x cubed you take the sign that's in front of it or you can change it to disinfecting the opposite you can write it like this you want or you can just take the whole tournament taking it with it so what is the degree of a term third degree of the term looking above that example of the degree of a term 5 x to the third plus 2X to  the degree of this term would be 3 the degree of the second term would be a 6 so the degree of a term is the exponent of the variable of the term the exponent of the variable of the turn so the degree of the first term Wikipedia what first turn right there it would be a or and the degree of the second term the second term Cafe by Walmart but it's A3 and the degree of the third term you can't see it but there's a one there the degree of the third term that one and then lastly what's the degree of this term right here we can't see an axe but there's understood to be an ex there What's Understood to be there tree of fourth term this could be written as the sum of 8 x 108 times x to the 0 power because I cuz your particles one so that would be zero so then what is the degree of a whole polynomial so that's looking at are examples 5x the fourth minus 3x squared plus 2X minus 8 sorry about that looking at this one what's the degree of that you guys think it's for or do you think it's for so 47828 well the answer is that the so the degree polynomial is for the definition is it is the degree term with largest exponent Forex celebrities who look like their look for the one with the largest exponent which happens to be a 4 to look at the second one what is that one going to be and you're probably still writing right now so keep writing the degree is yes you are correct 3 look at that time right there so what is standard form for a polynomial standard form for a polynomial it's terms are written in what type of order your steps and you were going down there if you're going down steps you are yes descending steps so it's terms are written and descending order of the variables expense so does any means from largest to smallest largest to smallest I need to write that down if you don't know what to say means sweetheart well there are you going to find the term with the largest export that's going to go first so I like to Circle them as I go so I don't forget any so negative effects of forthwith ghost next yep take a fine with it 5 x 2/3 and the next one is negative 2X and lastly -8 * 20 in standard okay cool fish ain't looking at that one above their the coefficient when we rewrote it at the first term as what yes that would be a -1 let's go fishing right here do you need a one confession of the second term 5 coconut the third term negative to quotation of the last term is -8 that's correct so real quick review and so you would probably tell me that the coefficient is the number that is in front of the variable and that's true that's what you were taught in Algebra 1 but there is you're going to notice that sometimes it's not always in the front so what's the coefficient it's the number in front of the variable so let's look at our example here is usually it's the number in front of the variable so the number in front of here would be -1x cubes so that coefficient would be a -1 and in this number oh it's not front of it but it's the numerical part right here so this one would be one and the number and try this one the one that you can I rewrite that as a square root of 6 times x yes I could but that's not good for him so here the number is not in front it's beside it and so that coefficient is a positive 3 and this last one will be and -8 so usually it is the number in front of the variable we have another definition it is the numerical number factor of a term documentation of patient going on so right here you see that multiplication going on right there so it would be discarded 3 multiplication right here also and that should be a review Okay so try to spice up because I know it's really difficult this is basically a long lesson on vocabulary different color exciting what is the leading coefficient coefficient obviously is a coefficient and it is the coefficient of the term that's in front when it is what form yep when it is in Cove when it is in standard form so it's the coefficient of the first term 10 in standard form have to be standard form so looking at the examples crawfish in here would be a negative 1/2 it is in standard form I noticed they're going down and decree to the terms so that number in front is going to be a negative one half and looking at the second one is that in standard form no, let's write in standard form Becky G of x equals negative X Cube square root of 5 exercise with it plus 2x squared Why is x + 7 so this is our first time what's the numerical Factor we have two parts to it we have the negative and then we have the square to 5 so leading coefficient on this one is negative square root of 5 so what is the constant term I looking at backup at that the previous one up here the constant term is what yes you are correct it's the negative 8th so some of the guys might say it is the term without a what is a term without visible variable so I don't see an X there but there is and xrx the zero power is this one the term without the physical therapy or you can say is the term that's just a number and that's usually the one that people kind of like I'm looking at are examples of squared minus 3x minus 9 what is the constant constant -9 and the second one over here but the constant there we don't see it so it would be 0 and why do you think it's called a constant that is constant mean never changes okay so it's called the constant because it does not change expression is evaluated for different X I use so it does not change when did expression is evaluated 4 different X values send example to x squared plus x minus one let's evaluate this when x equals 2 and x equals 1 so if I put two in there I'm going to get 2 x 4 which is 8 + 2 - 1 and when I plug the one in here I'm going to get two plus one -1 + what do you notice about this constant right here it changes but with the terms these are constantly changing so constant is a term that doesn't change so what is a polynomial function polynomial function can be written like this and you look at it it looks overwhelming but not that scary because that's a you say and is 6 then this would be a  that would be a 6 in here that's going to be a five and then they put a 6 in there that's for you put continue on to get down you would have the next to the 3rd and then you have your x squared x the first and your ex's Euro Car so basically all that is is a more difficult way to write with a polynomial with the polynomial function would be and as a two sticks that's just the coefficient XXX this is just a coefficient for the term where the acts as a power of 5 and so on so it's just a way of telling which coefficient text value a polynomial function obviously said equal to y or ever backs and the coefficients if you looked at where to look at all the coefficients they would be real numbers so you're not going to have any imaginary imaginary numbers for polynomial functions an exponent if you look up here we had  and I could be higher at 10 7 whatever and then 6 5 4 3 2 1 0 represented to the 10th power but you know those numbers 6 5 4 3 2 1 they're out there what type of numbers skip whole numbers and whole numbers are 0 1 2 3 excetera and I called whole numbers have to remember that actually and that the whole numbers include it a 0 o and 0 in the same Sun example y equals 2 Pi Pi located because pie is a real number irrational you can have a fraction you can have a decimal and you can have radical and there's a good answer Point example they move along what is the between a polynomial expression and a function and expression would be something like this 2 x squared minus 5x plus one and a function would be 2x squared minus 5x plus 1 equals y or ethics so expression polynomial expression that is has no equal sign where a polynomial function as equals y or Kohl's at the facts so you know he asked if polynomial functions if equation is not a polynomial function you're going to circle what makes it not one and then State the reason for your choice and I'll remember you going to check to see if exponents of the variables are what type of numbers decks bonds are what whole numbers and if the coefficients are not imaginary but real numbers so no I let's go through here at the first one FFX check the exponents I'll good as X20 those are whole numbers so the exponents art for the variables are whole numbers and then the coefficients we have square to 5 which is a real number three is real number that's a real number so coefficients are reels so all is good and so that would definitely be a polynomial function next one is check this one out we I don't even need to check and see if the exponents of variables are whole numbers and I was right there so efficient imaginary number so that's a big No-No and circle it and and let's check and see if the expense of variables are whole numbers yes but this one remember but the square 2x can be Rewritten as x to the one half power and so that number no sew Circle dots inside a radical it's it not a whole number for the exponent so on the exponent variable is not real I mean is not a whole number trust no Circle it and then make sure you  on that one minutes check Jetix exponent is a 4 and this one is a one here even though we don't write it so the Xbox are all good so the exponents are real Kitchen Grill exponent are whole numbers coefficients to 1/3 -pi is a number is irrational and one is good so that looks like that is a the variables are whole numbers and the coefficients are real numbers so I'll answer. Circle anything are you sure clean the things that make it not next one right away do you see what's wrong with it that's a no and why is that you have an Xbox at the negative to negative 2 is not a whole number that is for your exponents variable good Sentinel it Sucka in the back looks like the variables are okay for the next month of the variables are cakes set to remember that explanation when power is the same as what cracks so that can be Rewritten like that there for that explains the negative one so that would be a no cuz that exponent of the variable is -1 I did that to that when it printed okay that's a big bummer look like that okay so let's go ahead and take care of this and enter text I try to remember what to do here okay so this is what your sizes and I'm not stopping this so this is degree and this is the name the type this is example so the first example is y equals 5 and what is the degree of that will I can write 5 as five times 1 which is 5 times x to the 0 power that degree of zero and you know what type it is okay that's what I thought when later this is the next one y equals 8 x + 5 + the degree of that is quick the Mundo one and should know that when you have a degree of one that is called a what when you graph it is a line so that's linear and then you have written down here at y equals 8 x squared what type of polynomials yes you should know that one quadratic that degree is to here here and the next we have written down as y equals 8 x 2/3 + 5 + 2 degree of that one that is a 3 and Disney want to know what that's called House of the sea cubic and the next one you have written down is that what degree is that correct that is a for and if gallon of milk in divided into force it is a court for that score Tech and the next one you have written down is this one and the degree is 5 if you were to have 5 babies at what time they called it quits and if you have this one what degree is and that would be heck Tech not really it is a joke hahaha but you can keep their same for all of them but we're not going to do higher than 5 so I think we're going to do we're almost done and it is to this is the type of Pontiacs going to stay on your homework I'm going to ask different questions so the question is what type of question might be asking your homework you may be asked is the funk polynomial if it is not one then you're going to circle the part of the function that makes it not one and whatever your answer explain the reason for your choice but if the function is polynomial you can express it first thing in standard form and then you're going to stay it's degree and then you're going to State the leading coefficient and then you're going to State what type of function it is cubed kordic quintic hectic so we don't have that Victory and and according to the degree so let's look at that first one let's check the Expo to the variables are those whole numbers to the sexes europower and then 342 so those are good there's a whole numbers and then you can check coefficients so confessions the check those out I have a 7 as a real number 5 is rule number one fourth is real number that is 1/4 and then we have negative square root of 3 that's a rational but it's real number so we have real numbers so that's great that means we get a whole lot of work to do for homework first thing you're going to do is going to write it in standard form so you look for the highest degree which would be the X fourth and you're going to move that to the front take time with it and then look for next agree that's a little smaller Circle. So you don't forget it then the next one it's just a second term and then we don't have the extra the first but we have X's real power to standard form okay the next thing you're going to do is states to Greece what's the degree of that function polynomial function remember you don't add them all up the degrees at the Edibles up all you do is you find the largest one so it's going to be 4 so the degree of that function is for then you're going to State the leading coefficient which is the number in front and looks like that one right there so it's good note this right here so negative 1/4 when you're writing it and stand don't put that negative one there but that does help us figure out what the leading coefficient is and then lastly what type of function is that well it's the degree of four so that would be 4 gallons 1 gallon has how many what has 4 quarts to a zit cortic and we just got done what's thing you're going to do is you're going to look at this and check this one now and let's check the exponents I don't even need to check that it's because at my I caught something to do I catch something the coefficient is a -3 I so not real so therefore you would say that this is a not a polynomial function cuz it has an imaginary number coefficient which is actually the constant so that would be a no no in a pair of clutch right yes that it is a polynomial function and you are done with the most difficult lesson of the are you here because it's just a bunch of vocabulary your assignment assign it as 4.1 day 1 page 162 163 number to through 10 off and the 210 I think 3 through 10 are just like the ones we just did right above and then 14 and 16 23 + 24 + 23 + 24 they have they're the ones where there's an air so you have to describe the air and then also fix the air I think that's it you'll be working on correcting your chapter 3 packet also for homework so correct chapter 3 Target and make your car Jensen red or green some other color besides for back and if it's you really bust the problem up then go ahead and get a separate piece of paper out and fix it on a separate piece of paper and practice notice that right there what you giving details okay we're done

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4.1 Day 1 - Polynomials ALGEBRA 2

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