Question

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

Answer 1

degree: `4th`; type: quartic polynomial;
leading coefficient = `3`; constant term: `1`

Explanation:

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

`f(x) = a_nx^n + a_(n-1)x^(n-1) + a_(n-2)x^(n-2)+.....+ a_1x + 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(x) = 3x^4 + 3x^2 -2x + 1`

Degree is `4th`
Coefficient of the `x^4` is `3`
There are `4` terms: quartic polynomial
The constant term is the last term without a variable: `1`