# How do you find the degree, leading term, the leading coefficient, the constant term and the end behavior of g(x)=3x^5-2x^2+x+1?

Jun 15, 2018

Degree: $8$
Leading term: $3 {x}^{5}$
Leading Coefficient: $3$
Constant: $1$
End behavior: See below in blue

#### Explanation:

The degree is the sum of the exponents on all terms. Our exponents are $5 , 2$ and $1$, which sum up to $8$. This is the degree of our polynomial $g \left(x\right)$.

The leading term of a polynomial is just the term with the highest degree, and we see this is $3 {x}^{5}$.

The leading coefficient is just the number multiplying the highest degree term. The coefficient on $3 {x}^{5}$ is $3$.

The constant term is just a term without a variable. In our case, the constant is $1$.

For end behavior, we want to consider what our function goes to as $x$ approaches positive and negative infinity.

In our polynomial $g \left(x\right)$, the term with the highest degree is what will dominate the end behavior. So let's take the limit of it:

$\textcolor{b l u e}{{\lim}_{x \rightarrow \infty} 3 {x}^{5} = \infty}$

$\textcolor{b l u e}{{\lim}_{x \rightarrow - \infty} 3 {x}^{5} = - \infty}$

Our limits describe our limit behavior.

Hope this helps!