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

1 Answer
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#