Question

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

Answer 1

(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.