Question

Give the degree and leading coefficient of the following polynomial function. f(x)=x^7(7−6x^4−4x^4)

Answer 1

Degree is 11

Leading coefficient is -10

Explanations:

The highest value of the power of a given polynomial function is the degree of the function while the leading coefficient is the coefficient of the leading term.

Given the function

`\begin{gathered} f(x)=x^7(7-6x^4-4x^4) \\ f(x)=x^7(7-10x^4) \end{gathered}`

Expand the result

`\begin{gathered} f(x)=7x^7-10(x^(7+4)) \\ f(x)=7x^7-10x^(11) \end{gathered}`

Rearrange the resulting function according to the leading degree

`f(x)=-10x^(11)+7x^7`

From the resulting function, the degree of the polynomial is 11 while the leading coefficient is -10