Question

Classify the following polynomial based on their degree.

$3x^2+2x+1$

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.

Let $p\left(x\right)=3x^2+2x+1$

The degree of a polynomial is the highest power of $x$ in its expression.

Constant (non-zero) polynomials, linear polynomials, quadratics, cubics and quartics are polynomials of degree 0, 1, 2 , 3 and 4 respectively.

Highest power of $x$ in $p\left(x\right)$ is $=2$

Thus, the degree of $p\left(x\right)$ is $2$.

Hence, it is a quadratic polynomial.