Q17. - Algebra 2

Question

State the degree and leading coefficient of polynomial $\left(a+1\right)\left(a^2-4\right)$ in one variable. If it is not a polynomial in one variable, explain why.

Step-by-Step Solution

Answer

The polynomial has degree $3$ and leading coefficient $1$.

Step 1. Write down the given information.

The given polynomial is $\left(a+1\right)\left(a^2-4\right)$.

Step 2. Calculation.

Re-arranging the given polynomial $\left(a+1\right)\left(a^2-4\right)$ in descending order of degree.

$\left(a+1\right)\left(a^2-4\right)=a^3+a^2-4a-4$

Now, the degree and leading coefficient of the polynomial $a^3+a^2-4a-4$ are stated as:

The polynomial $a^3+a^2-4a-4$ is a polynomial in one variable $\left(a\right)$. Therefore, by concept of degree and leading coefficient of a polynomial, the degree of the polynomial is $3$ and leading coefficient is $1$.

Step 3. Conclusion.

The polynomial has degree $3$ and leading coefficient $1$.