Question

Is the function a polynomial if so state its degree and leading coefficient i know the degree is 5 but i just need the leading coefficient i believe its -7 but not sure

Answer 1

f(x) = 4 - 7x^5 is a polynomial,

degree = 5; and

leading coefficient = -7

Explanation:

A function, such as a quadratic, a cubic, a quartic, is a polynomial function which involves the integer powers of x that are non-negative.

So this definition applies to the given function f(x) = 4 - 7x^5 which involves a non-negative exponent, therefore it is a polynomial.

To find the degree of a polynomial, you look for the highest power in in the function, which here is 5.

The leading coefficient of a polynomial is the coefficient of the term with the highest power. Here the the term -7x^5 has the highest power so -7 is the leading coefficient.

Answer 2

Answer: f(x) is a polynomial. The degree is 5 and the leading coeficient is -7.

Explanation:

1. By definition a polynomial is the sum of terms that consist of a number (which is called "coefficient") that multiplies a variable with an exponent (This exponent is a whole number). Therefore, the function
`4-7x^(5)` is a polynomial.

2. To find the degree of the polynomial you must see the greatest exponent. In this case, this is 5. Therefore, the degree is 5.

3. The leading coefficient is the number that multiplied the variable with the greatest exponent. Therefore, the leading coefficient is -7.