Question

Which of the following expression are polynomials in one variable and which are non? Give reasons for your answer.
(i) $3x^2-2x+5$
(ii) $x^2+\sqrt{2}$
(iii) $p^2-3p+q$
(iv) $y+\frac{2}{y}$
(v) $5\sqrt{x}+x\sqrt{5}$
(vi) $x^{100}+y^{100}$

Answer 1

$\left(i\right)3x^2-2x+5$ Polynomial is one variable

Here $x$ is the only variable.

$\left(ii\right)x^2+\sqrt{2}$ Polynomial is one variable

Here $x$ is the only variable.

$\left(iii\right)p^2-3p+q$ Polynomial with two variables.

Here $p\&q$ are variables.

$\left(iv\right)y+\frac{2}{y}$ Not a polynomial

$\because y$ is having $-ve$ power in second term.

$\left(v\right)5\sqrt{x}+x\sqrt{5}$ Not a polynomial

$\because x$ is having fractional power in first term.

$\left(vi\right)x^{100}+y^{100}$ Polynomial with two variables.

Here $x\&y$ are variables.