For Exercises 1–4, (a) give the degree of the polynomial and (b) give the leading coefficient. 1. 3 x 4 − 5 x 2 + 2 3

Question

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Answer 1

Textbook Question

Chapter 6, Problem 1TE

For Exercises 1–4, (a) give the degree of the polynomial and (b) give the leading coefficient.

1. $3 x 4 − 5 x 2 + 2 3$

(a)

Expert Solution

To determine

To give: The degree of the polynomial $3x4−5x2+23$ .

Answer to Problem 1TE

The polynomial $3x4−5x2+23$ is a fourth degree polynomial.

Explanation of Solution

Formula used:

General form of polynomial:

“1. The general form of the polynomial is given by $anxn+an−1xn−1+⋯+a1x+a0$ , where $a0$ and each coefficient of x are real numbers and each power of x is positive integer.

2. If $an≠0$ , n is the highest power of x, $an$ is called the leading coefficients and n is the degree of the polynomial”.

Calculation:

The given polynomial $3x4−5x2+23$ which is in the form of $anxn+an−1xn−1+⋯+a1x+a0$ , where n is the degree of the polynomial.

The polynomial $3x4−5x2+23$ has the highest power term as $3x4$ and is of degree 4.

Therefore, the polynomial $3x4−5x2+23$ is a fourth degree polynomial.

(b)

Expert Solution

To determine

To give: The leading coefficient of the polynomial $3x4−5x2+23$ .

Answer to Problem 1TE

The leading coefficient of the polynomial $3x4−5x2+23$ is 3.

Explanation of Solution

From the polynomial $3x4−5x2+23$ , it is noted that the highest degree term is $3x4$ and its coefficient is 3.

By the above definition (2), it is known that if $an≠0$ , n is the highest power of x and $an$ is called the leading coefficients.

Therefore, the leading coefficient is 3 which is the coefficient of highest degree term.

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31.

Answer 2

Textbook Question

Chapter 6, Problem 1TE

For Exercises 1–4, (a) give the degree of the polynomial and (b) give the leading coefficient.

1. $3 x 4 − 5 x 2 + 2 3$

(a)

Expert Solution

To determine

To give: The degree of the polynomial $3x4−5x2+23$ .

Answer to Problem 1TE

The polynomial $3x4−5x2+23$ is a fourth degree polynomial.

Explanation of Solution

Formula used:

General form of polynomial:

“1. The general form of the polynomial is given by $anxn+an−1xn−1+⋯+a1x+a0$ , where $a0$ and each coefficient of x are real numbers and each power of x is positive integer.

2. If $an≠0$ , n is the highest power of x, $an$ is called the leading coefficients and n is the degree of the polynomial”.

Calculation:

The given polynomial $3x4−5x2+23$ which is in the form of $anxn+an−1xn−1+⋯+a1x+a0$ , where n is the degree of the polynomial.

The polynomial $3x4−5x2+23$ has the highest power term as $3x4$ and is of degree 4.

Therefore, the polynomial $3x4−5x2+23$ is a fourth degree polynomial.

(b)

Expert Solution

To determine

To give: The leading coefficient of the polynomial $3x4−5x2+23$ .

Answer to Problem 1TE

The leading coefficient of the polynomial $3x4−5x2+23$ is 3.

Explanation of Solution

From the polynomial $3x4−5x2+23$ , it is noted that the highest degree term is $3x4$ and its coefficient is 3.

By the above definition (2), it is known that if $an≠0$ , n is the highest power of x and $an$ is called the leading coefficients.

Therefore, the leading coefficient is 3 which is the coefficient of highest degree term.

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Answer 3

Textbook Question

Chapter 6, Problem 1TE

For Exercises 1–4, (a) give the degree of the polynomial and (b) give the leading coefficient.

1. $3 x 4 − 5 x 2 + 2 3$

(a)

Expert Solution

To determine

To give: The degree of the polynomial $3x4−5x2+23$ .

Answer to Problem 1TE

The polynomial $3x4−5x2+23$ is a fourth degree polynomial.

Explanation of Solution

Formula used:

General form of polynomial:

“1. The general form of the polynomial is given by $anxn+an−1xn−1+⋯+a1x+a0$ , where $a0$ and each coefficient of x are real numbers and each power of x is positive integer.

2. If $an≠0$ , n is the highest power of x, $an$ is called the leading coefficients and n is the degree of the polynomial”.

Calculation:

The given polynomial $3x4−5x2+23$ which is in the form of $anxn+an−1xn−1+⋯+a1x+a0$ , where n is the degree of the polynomial.

The polynomial $3x4−5x2+23$ has the highest power term as $3x4$ and is of degree 4.

Therefore, the polynomial $3x4−5x2+23$ is a fourth degree polynomial.

(b)

Expert Solution

To determine

To give: The leading coefficient of the polynomial $3x4−5x2+23$ .

Answer to Problem 1TE

The leading coefficient of the polynomial $3x4−5x2+23$ is 3.

Explanation of Solution

From the polynomial $3x4−5x2+23$ , it is noted that the highest degree term is $3x4$ and its coefficient is 3.

By the above definition (2), it is known that if $an≠0$ , n is the highest power of x and $an$ is called the leading coefficients.

Therefore, the leading coefficient is 3 which is the coefficient of highest degree term.

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Answer 4

Textbook Question

Chapter 6, Problem 1TE

For Exercises 1–4, (a) give the degree of the polynomial and (b) give the leading coefficient.

1. $3 x 4 − 5 x 2 + 2 3$

(a)

Expert Solution

To determine

To give: The degree of the polynomial $3x4−5x2+23$ .

Answer to Problem 1TE

The polynomial $3x4−5x2+23$ is a fourth degree polynomial.

Explanation of Solution

Formula used:

General form of polynomial:

“1. The general form of the polynomial is given by $anxn+an−1xn−1+⋯+a1x+a0$ , where $a0$ and each coefficient of x are real numbers and each power of x is positive integer.

2. If $an≠0$ , n is the highest power of x, $an$ is called the leading coefficients and n is the degree of the polynomial”.

Calculation:

The given polynomial $3x4−5x2+23$ which is in the form of $anxn+an−1xn−1+⋯+a1x+a0$ , where n is the degree of the polynomial.

The polynomial $3x4−5x2+23$ has the highest power term as $3x4$ and is of degree 4.

Therefore, the polynomial $3x4−5x2+23$ is a fourth degree polynomial.

(b)

Expert Solution

To determine

To give: The leading coefficient of the polynomial $3x4−5x2+23$ .

Answer to Problem 1TE

The leading coefficient of the polynomial $3x4−5x2+23$ is 3.

Explanation of Solution

From the polynomial $3x4−5x2+23$ , it is noted that the highest degree term is $3x4$ and its coefficient is 3.

By the above definition (2), it is known that if $an≠0$ , n is the highest power of x and $an$ is called the leading coefficients.

Therefore, the leading coefficient is 3 which is the coefficient of highest degree term.

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Answer 5

Textbook Question

Answer 6

Textbook Question

Answer 7

(a)

Expert Solution

To determine

To give: The degree of the polynomial $3x4−5x2+23$ .

Answer to Problem 1TE

The polynomial $3x4−5x2+23$ is a fourth degree polynomial.

Explanation of Solution

Formula used:

General form of polynomial:

“1. The general form of the polynomial is given by $anxn+an−1xn−1+⋯+a1x+a0$ , where $a0$ and each coefficient of x are real numbers and each power of x is positive integer.

2. If $an≠0$ , n is the highest power of x, $an$ is called the leading coefficients and n is the degree of the polynomial”.

Calculation:

The given polynomial $3x4−5x2+23$ which is in the form of $anxn+an−1xn−1+⋯+a1x+a0$ , where n is the degree of the polynomial.

The polynomial $3x4−5x2+23$ has the highest power term as $3x4$ and is of degree 4.

Therefore, the polynomial $3x4−5x2+23$ is a fourth degree polynomial.

(b)

Expert Solution

To determine

To give: The leading coefficient of the polynomial $3x4−5x2+23$ .

Answer to Problem 1TE

The leading coefficient of the polynomial $3x4−5x2+23$ is 3.

Explanation of Solution

From the polynomial $3x4−5x2+23$ , it is noted that the highest degree term is $3x4$ and its coefficient is 3.

By the above definition (2), it is known that if $an≠0$ , n is the highest power of x and $an$ is called the leading coefficients.

Therefore, the leading coefficient is 3 which is the coefficient of highest degree term.

Answer 8

(a)

Expert Solution

To determine

To give: The degree of the polynomial $3x4−5x2+23$ .

Answer to Problem 1TE

The polynomial $3x4−5x2+23$ is a fourth degree polynomial.

Explanation of Solution

Formula used:

General form of polynomial:

“1. The general form of the polynomial is given by $anxn+an−1xn−1+⋯+a1x+a0$ , where $a0$ and each coefficient of x are real numbers and each power of x is positive integer.

2. If $an≠0$ , n is the highest power of x, $an$ is called the leading coefficients and n is the degree of the polynomial”.

Calculation:

The given polynomial $3x4−5x2+23$ which is in the form of $anxn+an−1xn−1+⋯+a1x+a0$ , where n is the degree of the polynomial.

The polynomial $3x4−5x2+23$ has the highest power term as $3x4$ and is of degree 4.

Therefore, the polynomial $3x4−5x2+23$ is a fourth degree polynomial.

Answer 9

(a)

Expert Solution

Answer 10

(a)

Expert Solution

Answer 11

Expert Solution

Answer 12

To determine

To give: The degree of the polynomial $3x4−5x2+23$ .

Answer 13

Answer to Problem 1TE

The polynomial $3x4−5x2+23$ is a fourth degree polynomial.

Answer 14

Explanation of Solution

Formula used:

General form of polynomial:

“1. The general form of the polynomial is given by $anxn+an−1xn−1+⋯+a1x+a0$ , where $a0$ and each coefficient of x are real numbers and each power of x is positive integer.

2. If $an≠0$ , n is the highest power of x, $an$ is called the leading coefficients and n is the degree of the polynomial”.

Calculation:

The given polynomial $3x4−5x2+23$ which is in the form of $anxn+an−1xn−1+⋯+a1x+a0$ , where n is the degree of the polynomial.

The polynomial $3x4−5x2+23$ has the highest power term as $3x4$ and is of degree 4.

Therefore, the polynomial $3x4−5x2+23$ is a fourth degree polynomial.

Answer 15

(b)

Expert Solution

To determine

To give: The leading coefficient of the polynomial $3x4−5x2+23$ .

Answer to Problem 1TE

The leading coefficient of the polynomial $3x4−5x2+23$ is 3.

Explanation of Solution

From the polynomial $3x4−5x2+23$ , it is noted that the highest degree term is $3x4$ and its coefficient is 3.

By the above definition (2), it is known that if $an≠0$ , n is the highest power of x and $an$ is called the leading coefficients.

Therefore, the leading coefficient is 3 which is the coefficient of highest degree term.

Answer 16

(b)

Expert Solution

Answer 17

(b)

Expert Solution

Answer 18

Expert Solution

Answer 19

To determine

To give: The leading coefficient of the polynomial $3x4−5x2+23$ .

Answer 20

Answer to Problem 1TE

The leading coefficient of the polynomial $3x4−5x2+23$ is 3.

Answer 21

Explanation of Solution

From the polynomial $3x4−5x2+23$ , it is noted that the highest degree term is $3x4$ and its coefficient is 3.

By the above definition (2), it is known that if $an≠0$ , n is the highest power of x and $an$ is called the leading coefficients.

Therefore, the leading coefficient is 3 which is the coefficient of highest degree term.

Answer 22

Ch. 6.1 - Graph the function h(x) = 3x3 + 5x2 x 10 on the...Ch. 6.1 - Graph the function f(x) = 2x3 3x2 6x on the...Ch. 6.1 - Prob. 3E Ch. 6.1 - Prob. 4E Ch. 6.1 - Prob. 5E Ch. 6.1 - Prob. 6E Ch. 6.1 - Prob. 7E Ch. 6.1 - Prob. 8E Ch. 6.1 - Prob. 9E Ch. 6.1 - Prob. 10E

For Exercises 1–4, (a) give the degree of the polynomial and (b) give the leading coefficient. 1. 3 x 4 − 5 x 2 + 2 3

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