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

1 Answer
marfre
Apr 27, 2017

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

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