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

Oct 31, 2015

$4 {x}^{3} , 4 , 3$

#### Explanation:

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:
$F \left(x\right) = 4 {x}^{3} + 3 {x}^{2} + 2 x + 5$

Now, look at the first term with the largest exponent ($4 {x}^{3}$). 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: $4 {x}^{3}$.

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