Question

Identify polynomials in the following:

(i) f(x) = 4x³ - x² - 3x + 7 

(ii) g(x) = 2x³ - 3x² +\(\sqrt{x}\) -1 

(iii) p(x) = \(\frac{2}{3}\)x² -  \(\frac{7}{4}\)x + 9 

(iv) q(x) = 2x² - 3x + \(\frac{4}{x}\) + 2 

(v) h(x) = x⁴ -  x\(\frac{3}{2}\)- + x - 1

(vi) f(x) = 2 + \(\frac{3}{x}\) + 4x

Answer 1

(i) f(x) = 4x³ - x² - 3x + 7 is a polynomial.

(ii) g(x) = 2x³ - 3x²+\(\sqrt{x}\)-1is not a polynomial as exponent of x in \(\sqrt{x}\) is not a positive integer.

(iii) ) p(x) = \(\frac{2}{3}\)x² - \(\frac{7}{4}\) x + 9 is a polynomial as all the exponents are positive integer.

(iv) q(x) = 2x² - 3x + \(\frac{4}{x}\) + 2 is not a polynomial as the exponent of x in \(\frac{4}{x}\) is not a positive integer.

(v) h(x) = x⁴ - x\(\frac{3}{2}\)+ x - 1 is not a polynomial as the exponent of x in \(-x^{3/2}\) is not a positive integer.

(vi) f(x) = 2+ \(\frac{3}{x}\) + 4x is not a polynomial as the exponent of x in \(\frac{3}{x}\) is not a positive integer.