Question

Identify polynomials in the following :

(i) f(x) = $4x^3-x^2$ - 3x + 7

(ii) g(x) = $2x^3-3x^2+\sqrt{x}-1$

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

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

(v) h(x) = $x^4-x^{\frac{3}{2}}+x-1$

(vi) f(x) = 2 +$\frac{3}{x}+4x$

Answer 1

(i) f(x) : It is a polynomial.

(ii) g(x) : It is not a polynomial as degree of $\sqrt{x}$ is not a positive integer.

(iii) p(x)=$\frac{2}{7}{x}^2-\frac{7}{4}x+9$ It is a polynomial.

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

= $2x^2-3x+4x^{-1}+2$

It is not a polynomial as degree of $4x^{-1}$ is not a positive integer.

(v) h(x) = $x^4-x^{\frac{3}{2}}$ + x -1

It is not a polynomial as degree of x is no a positive integer.

(vi) f(x) = 2 +$\frac{3}{x}+4x=2+3x^{-1}+4x$

It is not a polynomial as degree of $x^{-1}$ is not a positive integer.