# What is the degree, type, leading coefficient, and constant term of g(x)=3x^4+3x^2-2x+1?

Apr 27, 2017

degree: $4 t h$; type: quartic polynomial;
leading coefficient = $3$; constant term: $1$

#### Explanation:

For a polynomial in descending order (largest exponent first):

$f \left(x\right) = {a}_{n} {x}^{n} + {a}_{n - 1} {x}^{n - 1} + {a}_{n - 2} {x}^{n - 2} + \ldots . . + {a}_{1} x + {a}_{0}$

The degree is $n$

The leading coefficient is ${a}_{n}$

The constant term is ${a}_{0}$

The type is based on the number of terms:
$1$ term is a monomial
$2$ terms is a binomial
$3$ terms is a trinomial
$4$ terms is a quartic polynomial
$4$ or more terms is called a polynomial

Given: $g \left(x\right) = 3 {x}^{4} + 3 {x}^{2} - 2 x + 1$

Degree is $4 t h$
Coefficient of the ${x}^{4}$ is $3$
There are $4$ terms: quartic polynomial
The constant term is the last term without a variable: $1$