Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer.
(i) 4x2 – 3x + 7
(ii) y2 + √2
(iii) 3√t + t√2
(i) 4x2 – 3x + 7
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
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
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.