Question

write the polynomial in standard form. then find its degree and the leading coefficient.
2w - w^{7} + 0.6w^{4} - 9.1

write the polynomial in standard form. select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. the standard form of the polynomial is
(use integers or decimals for any numbers in the expression.)
b. the polynomial is already in standard form.
the degree of the polynomial is
(type a whole number.)
the leading coefficient of the polynomial is
(type an integer or a decimal.)

Explanation:

Step1: Rearrange terms by degree

A polynomial in standard form is arranged in descending order of the exponents of the variable. The given polynomial is \(2w - w^{7}+ 0.6w^{4}- 9.1\). The exponents of \(w\) are \(1\), \(7\), \(4\), and \(0\) (for the constant term \(-9.1\)). Rearranging in descending order of exponents, we get \(-w^{7}+ 0.6w^{4}+ 2w - 9.1\).

Step2: Find the degree

The degree of a polynomial is the highest power of the variable. Here, the highest power of \(w\) is \(7\), so the degree is \(7\).

Step3: Find the leading coefficient

The leading coefficient is the coefficient of the term with the highest degree. The term with the highest degree (\(w^{7}\)) has a coefficient of \(-1\).

Answer:

The standard form of the polynomial is \(-w^{7}+ 0.6w^{4}+ 2w - 9.1\). The degree of the polynomial is \(7\). The leading coefficient of the polynomial is \(-1\).