State whether true/false: The following expression is a polynomial in one variable: $x^{10}+ y^3+ t^{50}$
$a.$ True $b.$ False
Answer
Clearly, the given expression $x^{10}+ y^3+ t^{50}$ contains three variables $x, y, t$ and $t$
Hence, the given expression is not a polynomial in one variable instead in three variables.
State True or False, if the following expression is polynomial in one variable $($State reason for your answer$): \text{y}+\frac{2}{\text{y}} \ a.$ True $b.$ False
Answer
The expression $\text{y}+\frac{2}{\text{y}}$ contain the term $\frac{2}{\text{y}},$
Here the exponent of y is $-1$, which is not a whole number.
Therefore, the given expression is not a polynomial in one variable.
State True or False, if the following expression is polynomial in one variable $4x^2- 3x + 7 \ a.$ True $b.$ False
Answer
Clearly, the expression $4x^2- 3x + 7$ is a polynomial in one variable x because there is only one variable $x$ in the expression having the highest power $2,$ which is
whole number.
State True or False, if the following expression is polynomial in one variable. $3\sqrt{\text{t}}+\text{t}\sqrt{2} \ a.$ True $b.$ False
Answer
The expression $3\sqrt{\text{t}}+\text{t}\sqrt{2}$ contain the term $3\sqrt{\text{t}},$
Here exponent of t is $\frac{1}{2}$ which is not a whole number.
Therefore, the given expression is not a polynomial in one variable.
State True or False, if he following expression is polynomial in one variable $\text{y}^2+\sqrt{2}\ a.$ True $b.$ False
Answer
Clearly, the expression $\text{y}^2+\sqrt{2}$ is a polynomial in one variable $y$ because there is only one variable $y$ in the expression having the highest power $2$, which is whole
number.