Chapter 6.8, Problem 22SGR

To determine

To calculate: The degree and leading coefficient of polynomial $5x^6-3x^4+x^3-9x^2+1$ if polynomial is not in one variable form then explain why is polynomial is not in one variable.

Answer to Problem 22SGR

The polynomial is in one variable form, the degree of polynomial is 6 and the leading coefficient of polynomial is 5.

Explanation of Solution

Given information:

The polynomial is given as:

  $5x^6-3x^4+x^3-9x^2+1$

Formula used:

The polynomial in one variable is in the form as, $a_n{x}^n+a_{n-1}{x}^{n-1}+\mathrm{.....}+a_{1}x+a_0$ where $a_0\ne 0$ , $a_{n-1},a_{n-2},\mathrm{.....},a_1$ and $a_0$ are real numbers and $n$ is a nonnegative integer.

The degree of polynomial is degree of the monomial with the greatest degree.

The coefficient of the first term of a polynomial is know the leading coefficient.

Calculation:

First check the polynomial is in one variable or not as,

The provided polynomial $5x^6-3x^4+x^3-9x^2+1$ is in one variable form.

The degree of polynomial $5x^6-3x^4+x^3-9x^2+1$ is 6 because the monomial with greatest degree is 5.

The leading coefficient of the polynomial $5x^6-3x^4+x^3-9x^2+1$ is 5 because the coefficient of first term is 5.