 Hello and welcome to the session. In this session we will discuss polynomials in one variable. A polynomial Px in one variable x is an algebraic expression in x of the form Px equal to an into x to the power n plus an minus 1 into x to the power n minus 1 plus and so on up to a2 x square plus a1x plus a0 that is this Px is a polynomial in one variable that is x. Where we have these a0 a1 a2 and so on up to an are the constants and we have an is not equal to 0 then these a0 a1 a2 and so on up to an are respectively the coefficients of x0 xx square and so on up to x to the power n and switch off an into x to the power n an minus 1 into x to the power n minus 1 and so on up to a0 where we have an is not equal to 0 is called the term of the polynomial Px. The constant polynomial 0 is called the 0 polynomial. Now let's define the degree of the polynomial highest power of the variable in a polynomial is called the degree of the polynomial. Now the degree for this polynomial Px is given by n that is we say that degree of Px is equal to n and also degree of a nonzero constant polynomial is 0. Consider a polynomial 2 this is a nonzero constant polynomial so degree for this polynomial would be 0. Let's consider a polynomial Px equal to 5x cube plus 4x square plus 7x then we have degree of Px is equal to 3 since 3 is the highest power of the variable of the polynomial. Then we have a polynomial with one term is called a monomial like for example we have 3x this is a monomial since it has only one term then a polynomial with two terms is called a binomial for example 2 plus 3x this expression has two terms that is 2 and 3x and therefore it's a binomial then a polynomial with three terms is called a trinomial for example we have 2 plus 3x plus 6x square this expression has three terms 2, 3x and 6x square so it is a trinomial. Next we have polynomial of degree 1 is called a linear polynomial it is generally of the form ax plus b where we have a and b are the constants and a is not equal to 0 so this is a linear polynomial in variable x like for example we have 2x plus 3 this is a linear polynomial since we have degree for this polynomial is 1 then next we have a polynomial of degree 2 is called a quadratic polynomial and a quadratic polynomial in x is of the form ax square plus bx plus c where we have a b c are the constants and a is not equal to 0 an example of quadratic polynomial can be taken as 6x square plus 2x plus 3 then next we have a polynomial of degree 3 is called a cubic polynomial this can be generally written in the form ax cube plus vx square plus cx plus d where we have a b c and b are the constants and a is not equal to 0 an example for cubic polynomial can be taken as 3x cube plus 6x square plus 2x plus 3 as you can see a linear polynomial in x can have at most two terms then a quadratic polynomial in x can have at most three terms and the cubic polynomial in x can have at most four terms we know that a zero polynomial is denoted by zero and also degree of the zero polynomial is not defined next we discuss zeroes of a polynomial a real number a zero of a polynomial if we have pa is equal to zero and in this case this a is also called the root of the equation px equal to zero also a non-zero constant polynomial has no zero also we have that every real number a zero of the zero polynomial then we have some observations related to zero of the polynomial like we say that a zero of a polynomial need not be zero then zero maybe zero of a polynomial also we have that every linear polynomial one and only one zero and a polynomial can have more than one zero in a polynomial px equal to x minus three let's try and find out the zero of this polynomial for this we put px equal to zero that is we have x minus three is equal to zero which gives x equal to three so we say that three is the zero of the polynomial px this completes a session hope you have understood the concept of polynomials in one variable and how we find the zeroes of a polynomial