Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer.
(i) 4x 2 – 3x + 7
(ii) y 2 + √2
(iii) 3 √t + t√2
(iv) y +\(\frac{ 2 }{ y} \)
(v) x 10 + y 3 + t 50
Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer.
(i) 4x 2 – 3x + 7
(ii) y 2 + √2
(iii) 3 √t + t√2
(iv) y +\(\frac{ 2 }{ y} \)
(v) x 10 + y 3 + t 50
Solution and Explanation
(i) 4x2 - 3x + 7
Yes, this expression is a polynomial in one variable x.
(ii) y2 + √2
yes, this expression is a polynomial in one variable y.
(iii) 3 √t + t √2
No, it can be observed that the exponent of variable t in term 3√t \(\frac{ 1 }{ 2} \), is, which is not a whole number. Therefore, this expression is not a polynomial.
(iv) y + \(\frac{ 2 }{ y} \)
No, it can be observed that the exponent of variable y in term \(\frac{ 2 }{ y} \) is -1, which is not a whole number. Therefore, this expression is not a polynomial.
(v) x10 + y3 + t50
No, it can be observed that this expression is a polynomial in 3 variables, x, y, and t.
Therefore, it is not a polynomial in one variable.