Question:
Classify the following polynomials as polynomials in one variables, two - variables etc:
1. $x^{2}-x y+7 y^{2}$
2. $x^{2}-2 t x+7 t^{2}-x+t$
3. $t^{3}-3 t^{2}+4 t-5$
4. $x y+y z+z x$
Solution:
Given
1. $x^{2}-x y+7 y^{2}$ it is a polynomial in two variables $x$ and $y$
2. $x^{2}-2 t x+7 t^{2}-x+t$ it is a polynomial in two variables $x$ and $t$
3. $t^{3}-3 t^{2}+4 t-5$ it is a polynomial in one variable $t$
4. $x y+y z+z x$ it is a polynomial in 3 variables in $x, y$ and $z$