Question

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

(i) 3x² – 4x + 15 

(ii) y² + 2√3 

(iii) 3√x + √2x 

(iv) \(x - \frac{4}{x}\) 

(v) x¹² + y³ + t⁵⁰

Answer 1

(i) 3x² – 4x + 15 

It is a polynomial of x. 

(ii) y² + 2√3 

It is a polynomial of y. 

(iii) 3√x + √2x 

It is not a polynomial since the exponent of 3√x is a rational term. 

(iv) \(x - \frac{4}{x}\)

It is not a polynomial since the exponent of \(\frac{-4}{x}\) is not a positive term. 

(v) x¹² + y³ + t⁵⁰ 

It is a three variable polynomial, x, y and t.