Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer.

 (i) 4x2–3x+7

Solution:

The equation 4x2–3x+7 can be written as 4x2–3x1+7x0

Since x is the only variable in the given equation and the powers of x (i.e., 2, 1 and 0) are whole numbers, we can say that the expression 4x2–3x+7 is a polynomial in one variable.

(ii) y2+√2

Solution:

The equation y2+√2 can be written as y2+√2y0

Since y is the only variable in the given equation and the powers of y (i.e., 2 and 0) are whole numbers, we can say that the expression y2+√2 is a polynomial in one variable.

(iii) 3√t+t√2

Solution:

The equation 3√t+t√2 can be written as 3t1/2+√2t

Though, t is the only variable in the given equation, the powers of t (i.e.,1/2) is not a whole number. Hence, we can say that the expression 3√t+t√2 is not a polynomial in one variable.

(iv) y+2/y

Solution:

The equation y+2/y an be written as y+2y-1

Though, y is the only variable in the given equation, the powers of y (i.e.,-1) is not a whole number. Hence, we can say that the expression y+2/y is not a polynomial in one variable.

(v) x10+y3+t50

Solution:

Here, in the equation x10+y3+t50

Though, the powers, 10, 3, 50, are whole numbers, there are 3 variables used in the expression

x10+y3+t50. Hence, it is not a polynomial in one variable.