Question

State the degree and leading coefficient of polynomial $2b+4b^3-3b^5-7$ in one variable. If it is not a polynomial in one variable, explain why.

Short answer

The polynomial has degree 5 and leading coefficient $-3$.

Step-by-step solution

Step 1. Write down the given information.

The given polynomial is $2b+4b^3-3b^5-7$.

Step 2. Calculation.

Re-arranging the given polynomial in descending order of degree, the polynomial can be written as:

$-3b^5+4b^3+2b-7$

Now, the degree and leading coefficient of the given polynomial $5x^6-8x^2$are stated as:

The given polynomial is a polynomial in one variable $\left(b\right)$. Therefore, by concept of degree and leading coefficient of a polynomial, the degree of the polynomial is $5$ and leading coefficient is $-3$.

Step 3. Conclusion.

The polynomial has degree 5 and leading coefficient $-3$.