Chapter 4, Problem 1RE

To determine

The degree and leading coefficient of the polynomial $f\left(x\right)=4+x-2x^2-7x^3$ .

Answer to Problem 1RE

Solution: The degree of the polynomial is 3and the leading coefficient is $-7$ .

Explanation of Solution

Given: The polynomial $f\left(x\right)=4+x-2x^2-7x^3$ .

Calculation: To determine the degree and leading coefficient of the given polynomial, first we will write the polynomial in the descending order of exponents as shown below.

  $f\left(x\right)=-7x^3-2x^2+x+4$

Now, we can see that the term $-7x^3$ has the highest exponent as 3, and hence the degree of the polynomial is 3.

Since the term $-7x^3$ has the highest exponent, it is the leading term of the given polynomial. And, we can observe that the coefficient of $x^3$ in $-7x^3$ is $-7$ , hence the leading coefficient of the polynomial is $-7$ .

Conclusion: The degree of the polynomial is 3 and the leading coefficient is $-7$ .