Question

State the degree and leading coefficient of polynomial $7+3x^2-5x^3+6x^2-2x$ in one variable. If it is not a polynomial in one variable, explain why.

Short answer

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

Step-by-step solution

Step 1. Write down the given information.

The given polynomial is $7+3x^2-5x^3+6x^2-2x$.

Step 2. Calculation.

Re-arranging the given polynomial $7+3x^2-5x^3+6x^2-2x$ in descending order of degree, the polynomial can be written as $-5x^3+9x^2-2x+7$.

Now, the degree and leading coefficient of the polynomial $-5x^3+9x^2-2x+7$are stated as:

The polynomial $-5x^3+9x^2-2x+7$ is a polynomial in one variable $\left(x\right)$. Therefore, by concept of degree and leading coefficient of a polynomial, the degree of the polynomial is $3$ and leading coefficient is $-5$.

Step 3. Conclusion.

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