Question

State whether the following expression is a polynomial in one variable or not.

$2x^2-2x+1$

Answer 1

A polynomial is a function of the form $f\left(x\right)=a_n{x}^n+a_{n-1}{x}^{n-1}+...+a_2{x}^2+a_{1}x+a_0$ .

where $a_n,a_{n-1},...a_2,a_1,a_0$ . are contants

and $n$ is a natural number.

Given $p\left(x\right)=2x^2-2x+1$

According to above definition, $x$ is a variable

No. of variables $=1$

Hence, $P\left(x\right)$ is a polynomial in one variable.