Which of the following expressions are polynomials in one variable and

1.	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» (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.

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»

(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.