Which of the following expressions are polynomials in one variable and which are not?
Question:

Which of the following expressions are polynomials in one variable and which are not?

State the reasons for your answers

1. $3 x^{2}-4 x+15$

2. $y^{2}+2 \sqrt{3}$

3. $3 \sqrt{x}+\sqrt{2} x$

4. $x-4 / x$

5. $x^{12}+y^{2}+t^{50}$

Solution:

1. $3 x^{2}-4 x+15$ it is a polynomial of $x$

2. $y^{2}+2 \sqrt{3}$ it is a polynomial of $y$

$3 \sqrt{x}+\sqrt{2} x$ it is not a polynomial since the exponent of $3 \sqrt{x}$ is not a positive term

4. $x-4 / x$ – it is not a polynomial since the exponent of $-4 / x$ is not a positive term

5. $x^{12}+y^{2}+t^{50}$ it is a three variable polynomial which variables of $x, y, t$

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