The degree and leading coefficient of the polynomial f ( x ) = 4 + x − 2 x 2 − 7 x 3 .

Question

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Answer 1

Question

Chapter 4, Problem 1RE

To determine

The degree and leading coefficient of the polynomial f(x)=4+x−2x2−7x3 .

Expert Solution & Answer

Answer to Problem 1RE

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

Explanation of Solution

Given: The polynomial f(x)=4+x−2x2−7x3 .

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(x)=−7x3−2x2+x+4

Now, we can see that the term −7x3 has the highest exponent as 3, and hence the degree of the polynomial is 3.

Since the term −7x3 has the highest exponent, it is the leading term of the given polynomial. And, we can observe that the coefficient of x3 in −7x3 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 .

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Answer 2

Question

Chapter 4, Problem 1RE

To determine

The degree and leading coefficient of the polynomial f(x)=4+x−2x2−7x3 .

Expert Solution & Answer

Answer to Problem 1RE

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

Explanation of Solution

Given: The polynomial f(x)=4+x−2x2−7x3 .

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(x)=−7x3−2x2+x+4

Now, we can see that the term −7x3 has the highest exponent as 3, and hence the degree of the polynomial is 3.

Since the term −7x3 has the highest exponent, it is the leading term of the given polynomial. And, we can observe that the coefficient of x3 in −7x3 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 .

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Answer 3

Question

Chapter 4, Problem 1RE

To determine

The degree and leading coefficient of the polynomial f(x)=4+x−2x2−7x3 .

Expert Solution & Answer

Answer to Problem 1RE

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

Explanation of Solution

Given: The polynomial f(x)=4+x−2x2−7x3 .

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(x)=−7x3−2x2+x+4

Now, we can see that the term −7x3 has the highest exponent as 3, and hence the degree of the polynomial is 3.

Since the term −7x3 has the highest exponent, it is the leading term of the given polynomial. And, we can observe that the coefficient of x3 in −7x3 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 .

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Answer 4

Question

Chapter 4, Problem 1RE

To determine

The degree and leading coefficient of the polynomial f(x)=4+x−2x2−7x3 .

Expert Solution & Answer

Answer to Problem 1RE

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

Explanation of Solution

Given: The polynomial f(x)=4+x−2x2−7x3 .

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(x)=−7x3−2x2+x+4

Now, we can see that the term −7x3 has the highest exponent as 3, and hence the degree of the polynomial is 3.

Since the term −7x3 has the highest exponent, it is the leading term of the given polynomial. And, we can observe that the coefficient of x3 in −7x3 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 .

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Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 5

Chapter 4, Problem 1RE

To determine

The degree and leading coefficient of the polynomial f(x)=4+x−2x2−7x3 .

Expert Solution & Answer

Answer to Problem 1RE

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

Explanation of Solution

Given: The polynomial f(x)=4+x−2x2−7x3 .

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(x)=−7x3−2x2+x+4

Now, we can see that the term −7x3 has the highest exponent as 3, and hence the degree of the polynomial is 3.

Since the term −7x3 has the highest exponent, it is the leading term of the given polynomial. And, we can observe that the coefficient of x3 in −7x3 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 .

Answer 6

Chapter 4, Problem 1RE

To determine

The degree and leading coefficient of the polynomial f(x)=4+x−2x2−7x3 .

Expert Solution & Answer

Answer to Problem 1RE

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

Explanation of Solution

Given: The polynomial f(x)=4+x−2x2−7x3 .

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(x)=−7x3−2x2+x+4

Now, we can see that the term −7x3 has the highest exponent as 3, and hence the degree of the polynomial is 3.

Since the term −7x3 has the highest exponent, it is the leading term of the given polynomial. And, we can observe that the coefficient of x3 in −7x3 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 .

Answer 7

Chapter 4, Problem 1RE

To determine

The degree and leading coefficient of the polynomial f(x)=4+x−2x2−7x3 .

Answer 8

Expert Solution & Answer

Answer to Problem 1RE

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

Answer 9

Expert Solution & Answer

Answer 10

Expert Solution & Answer

Answer 11

Explanation of Solution

Given: The polynomial f(x)=4+x−2x2−7x3 .

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(x)=−7x3−2x2+x+4

Now, we can see that the term −7x3 has the highest exponent as 3, and hence the degree of the polynomial is 3.

Since the term −7x3 has the highest exponent, it is the leading term of the given polynomial. And, we can observe that the coefficient of x3 in −7x3 is −7 , hence the leading coefficient of the polynomial is −7 .