What is the leading term, leading coefficient, and degree of this polynomial #F(x) = 5 + 2x + 3x^2 + 4x^3#?

1 Answer
Oct 31, 2015

#4x^3, 4, 3#


First, you have to rewrite the equation in standard form (highest degree first, or largest exponent): Since 3 is the highest exponent, you would write that term first, then write the rest of the terms in decreasing order, based on exponent:
#F(x) = 4x^3 +3x^2 +2x + 5#

Now, look at the first term with the largest exponent (#4x^3#). The degree of the polynomial is the largest exponent, which is 3 in this polynomial.

Since this term has the highest exponent (degree of the polynomial), then it is also the leading term: #4x^3#.

Lastly, the leading coefficient is the number in front of the variable in the leading term, which is #4# in this case.