Q21. - Algebra 2

Question

State the degree and leading coefficient of polynomial $c^2+c-\frac{1}{c}$ in one variable. If it is not a polynomial in one variable, explain why.

Step-by-Step Solution

Answer

The given polynomial is not a polynomial because a polynomial can never contain negative exponent in it.

Step 1. Write down the given information.

The given polynomial is $c^2+c-\frac{1}{c}$.

Step 2. Calculation.

Re-arranging the given polynomial $c^2+c-\frac{1}{c}$ in descending order of degree, the polynomial can be written as $c^2+c-c^{-1}$.

Now, the polynomial $c^2+c-c^{-1}$ can-not have a negative exponent in its expression. Therefore, the given polynomial $c^2+c-\frac{1}{c}$ is not a polynomial.

Step 3. Conclusion.

The given polynomial is not a polynomial because a polynomial can never contain negative exponent in it.