 Hi and welcome to the session, I am Asha and I am going to help you solve this question of your NCRK textbook which says which of the following expressions are polynomials in one variable and which are not straight reasons for your answer. So, first let us learn what are polynomials. So, algebraic expressions that have only whole numbers at the exponent of the variables are called polynomials. The key idea we are going to use in this problem to find its solution. Starting with the first part which is 4x square minus 3x plus 7. Now, on observing this algebraic expression we find that where the variable is x and the powers of x in this expressions are 2 and 1 which are whole numbers. So, from a key idea any algebraic expression that have only whole numbers as exponents of the variables are called polynomials therefore this expression is a polynomial. So, let us write it down. The exponent of the variable x, one of whole numbers, the given expression 4x square minus 3x plus 7 is a polynomial. This completes the first part and now proceeding on to the next part which is y square plus root over 2. Now, on observing this algebraic expression we find that here the variable is y and the exponent of y is 2 which is a whole number therefore this expression is also a polynomial that is the exponent of the variable y is 2 which is a whole number therefore y square plus root over 2 is a polynomial. So, this completes the second part. Now, proceeding on to the next part which is 3 root over 3 plus t root 2 which can also be written as 3, t raise to the power half plus t root 2. Now, on observing this algebraic expression we find that here the variable is t, exponent of t the first term is half which is not a whole number. This algebraic expression is not a polynomial that is 3 root over t plus t root over 2 is not a polynomial since the exponent of t in the first term is half which is not a whole number. So, this completes the third part and now proceeding on to the next one where we have to find that y plus 2 upon y is a polynomial or not. So, this can be written as y plus 2 raise 2 into y raise to the power minus 1 and here the variable is y the exponents are 1 and minus 1 exponents of variable y 1 and minus 1 but minus 1 is not a whole number this implies the given algebraic expression is not a polynomial that is y plus 2 upon y is not a polynomial. So, this completes the fourth part and now proceeding on to the last one which is x raise to the power 10 plus y raise to the power 3 plus t raise to the power 50. Now, here we have 3 variables x, y and t are the variables exponents are 10, 3 and 50 respectively which are all whole numbers. Y raise to the power 10, y raise to the power 3 and t raise to the power 50 is a polynomial in 3 variables. Fifth part and hence our answers are 1 are polynomials in one variable and n is a polynomial in 3 variables. It's the solution hope you enjoyed this session take care and bye for now.