 Hi friends so continuing with our session on polynomials in this session We are going to discuss what all types of polynomials are You know what a polynomial is if you are not clear on that I would suggest you can go back to our Playlist and just watch the previous session. You'll get to know what polynomials are now in this session We are going to discuss different types of polynomials basis their degree, right? You know the degree what is the degree of a polynomial degree of a polynomial is nothing, but the power of the highest Degree term right is a degree of the polynomial. So first category or first type is nothing but constant polynomial constant Constant polynomial. So as the name suggests as the name suggests constant polynomial is nothing but a polynomial of degree zero What is it? polynomial so it is a Polynomial polynomial of degree zero that means it is a constant Degree zero so for example examples are let us say FX FX equals to let's say 91 okay, or GT in variable is T. So let us say 42 all are degree zero terms Right degree zero terms. So hence the they are called constant polynomial okay now There is there is one one concept called zero polynomial. So in this constant polynomial if the value is zero zero poly zero polynomial Right, what is a zero polynomial? So if you if any polynomial is that their FX equals to let's say zero it's called a zero polynomial But the problem is the degree of this is not defined degree of a zero polynomial degree of a zero zero polynomial is Not defined is not is not defined Okay, it's not defined Why because because if you see zero polynomial can be written as zero times x to the power one this can equal to zero This can is this can be equal to zero into x to the power two or this can be zero into x to the power 99 or whatever Right, it's very difficult to find out then what will be the degree of zero polynomial So please remember zero polynomial degree is not defined Okay, this is one one case now second is second category is linear polynomial So you have studied about linear polynomials time and again linear Polynomials, what are linear polynomial polynomials? So let us say and we are again going to deal only with one variable So Px is equal to let us say 7x minus 5. This is a Linear polynomial y because if you see the highest term degree term is 7x whose degree is one similarly gt is equal to let us say minus root 2 e plus 47 so here also this is linear polynomial or H y is equal to 40 70 Oh, sorry. It cannot be in T. It is it has to be let's say y so 47 y these are all These are all examples of Linear polynomials and if you notice the maximum number of terms in linear polynomials could be two only right So one will be the term containing x and the other could be the constant term. So maximum number of max number of terms possible in a linear linear polynomial is two then comes your very famous quadratic quadratic polynomial So you already know Or even if you don't know quadratic polynomials are nothing but polynomials of degree 2 so example Px is equal to root 2 x square minus 3x plus 4. This is one then qx Let us say is equal to 7x square this is also another where the other two terms are not there and let us say G of x is equal to let us say 5x square minus 27x all are All are examples of quadratic polynomial guys now here if you see again maximum number of terms possible is 3 maximum number of terms Is nothing but 2 plus 1 quadratic degree is 2 plus 1 is 3 Right, this is another understanding similarly on similar lines You can you know there is something called cubic Now cubic is nothing but degree will be 3 Degree is 3 so example Px Is equal to 3x cube minus 27x square plus 90x minus 7 Or gt could be let us say 3t cube minus 27t Right or h of let us say y is equal to y root 2 y root 2 y cube and Let's say that's it. So all these are Degree 3 and again max number if you see max number of terms You can now guess very easily Is nothing but 3 plus 1 is equal to 4 max It need not be having four terms all the time For example, if you see here only one term is there, but still it is Cubic why because the highest term highest degree term is This 3 Okay. Similarly, there are you know, you can have end number of This thing for example, the next one is by quadratic By quadratic where you have would have guessed by now degrees 4 degrees 4 And then there are things like quintic and so on and so forth. These are so sixth one is quintic where the degree is 5 so you would have now known if degrees 4 max number of terms is max terms max number of terms will be nothing but 5 and in this case max number of max number of terms will be 6 Understood. So this is one Categorization of polynomials. So we saw what all constant polynomials We saw zero polynomial. We saw linear polynomials quadratic polynomial cubic by quadratic and quintic all these polynomials in themselves have different different properties and all these properties will be studied under polynomials, okay So we'll be taking up in this particular series of sessions we'll be taking up talking about constant polynomial We'll be talking about linear quadratic and then cubic right and then we'll see What is meant by their zeros and other related properties