Q19. - Algebra 2

Question

State the degree and leading coefficient of polynomial $6x^4+3x^2+4x-8$ in one variable. If it is not a polynomial in one variable, explain why.

Step-by-Step Solution

Answer

The polynomial has degree $4$ and leading coefficient $6$.

Step 1. Write down the given information.

The given polynomial is $6x^4+3x^2+4x-8$.

Step 2. Calculation.

The given polynomial $6x^4+3x^2+4x-8$ is in decreasing order of degree.

Therefore, the degree and leading coefficient of the polynomial $6x^4+3x^2+4x-8$ are stated as:

The polynomial $6x^4+3x^2+4x-8$ 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 4 and leading coefficient is 6.

Step 3. Conclusion.

The polynomial has degree 4 and leading coefficient 6.