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 \(\sqrt{3}\)

(iii) 3 \(\sqrt{x}\) + \(\sqrt{2}\,\text{x}\)

(iv) \(x-\frac{4}{x}\)

(v) \(\text{x}^{12}+\text{y}^{3}+t^{50}\)

Answer 1

(i) 3x² - 4x + 15 is a polynomial of one variable x.

(ii) \(y^{2}+2\sqrt{3}\) is a polynomial of one variable y.

(iii) \(3\sqrt{x}+\sqrt{2}\) x is not a polynomial as the exponent of 3\(\sqrt{x}\) is not a positive integer.

(iv) \(x-\frac{4}{x}\) is not a polynomial as the exponent of -\(\frac{4}{x}\) is not a positive integer.

(v) \(x^{12}+y^{3}+t^{50}\) is a polynomial of three variables x, y, t.