DEGREE OF A POLYNOMIAL WORKSHEET

Problem 1-15 : In each case, find the degree of the given polynomial.

Problem 1 :

x⁴

Problem 2 :

7p³q²

Problem 3 :

-2xy²z³

Problem 4 :

2x + 5

Problem 5 :

7 - 3y

Problem 6 :

3p - 13p⁷

Problem 7 :

-7y⁴ + 3y - 13y³

Problem 8 :

3r² - r + r³

Problem 9 :

3z⁵ - 2z³ - z - 4

Problem 10 :

5y + √2

Problem 11 :

√3x + 1

Problem 12 :

x³ + √2x + 4x - 1

Problem 13 :

0.7pq² - 0.45pq + 0.33

Problem 14 :

0.25m²n + 3m³n⁵

Problem 15 :

a³b² + a²b³ - a⁴ + b⁴ + 3

Problem 16 :

Add the following two polynomials and find the degree of the resulting polynomial.

(2x² + 5xy + 9y²) and (-3x² - 5xy + 4y²)

Problem 17 :

Subtract (p⁴ - p² + 2p + 3) from (2p⁴ - 2p³ - 4p + 5) and find the degree of the resulting polynomial.

Problem 18 :

Simplify and find the degree of the resulting polynomial.

(3y² - 5z) - (y - 7z²) - (5y² - 6z²) + (3y + z)

Problems 19-20 : Form a binomial with the given description.

Problem 19 :

x with a degree of 2

Problem 20 :

x and y with a degree of 2

Problems 21-23 : Form a trinomial with the given description.

Problem 21 :

y with a degree of 2

Problem 22 :

k with a degree of 5

Problem 23 :

z with a degree of 4

Answers

1. Answer :

In x⁴, there is only one variable term with exponent 4.

So, the degree of the polynomial is 4.

2. Answer :

In 7p³q², there is only variable term with a product of two variables p and q.

The sum of exponents of p and q is 5.

That is,

3 + 2 = 5

So, the degree of the polynomial is 5.

3. Answer :

In -2xy²z³, there is only one variable term with a product of three variables x, y and z.

The sum of exponents of x, y and z is 6.

1 + 2 + 3 = 6

So, the degree of the polynomial is 6.

4. Answer :

The terms of the given polynomial are 2x and 5.

Exponent of each of the terms : 1, 0.

Terms with highest exponent : 2x¹.

Therefore, degree of the polynomial is 1.

5. Answer :

The terms of the given polynomial are 7 and -3y.

Exponent of each of the terms : 0, 1.

Terms with highest exponent : -3y¹.

Therefore, degree of the polynomial is 1.

6. Answer :

The terms of the given polynomial are 3p and -13p⁷.

Exponent of each of the terms : 1, 7.

Terms with highest exponent : -13p⁷.

Therefore, degree of the polynomial is 7.

7. Answer :

The terms of the given polynomial are -7y⁴, 3y, and -13y³.

Exponent of each of the terms : 4, 1, 3.

Terms with highest exponent : -7y⁴.

Therefore, degree of the polynomial is 4.

8. Answer :

The terms of the given polynomial are 3r², -r and r³.

Exponent of each of the terms : 2, 1, 3.

Terms with highest exponent : r³.

Therefore, degree of the polynomial is 3.

9. Answer :

The terms of the given polynomial are 3z⁵, -2z³, -z and -4.

Exponent of each of the terms : 5, 3, 1, 0.

Terms with highest exponent : 3z⁵.

Therefore, degree of the polynomial is 5.

10. Answer :

The terms of the given polynomial are 5y and √2.

Exponent of each of the terms : 1, 0.

Terms with highest exponent : 5y.

Therefore, degree of the polynomial is 1.

11. Answer :

The terms of the given polynomial are √3x and 1.

Exponent of each of the terms : 1, 0.

Terms with highest exponent : √3x.

Therefore, degree of the polynomial is 1.

12. Answer :

The given polynomial can be written as

x³ + (√2 + 4)x - 1

The terms of the given polynomial are x³, (√2 + 4)x and -1.

Exponent of each of the terms : 3, 1, 0.

Terms with highest exponent : x³.

Therefore, degree of the polynomial is 3.

13. Answer :

The terms of the given polynomial are 0.7pq², -0.45pq, 0.33.

Exponent of each of the terms : 3, 2, 1.

Terms with highest exponent : 0.7pq².

Therefore, degree of the polynomial is 3.

14. Answer :

The terms of the given polynomial are 0.25m²n and 3m³n⁵.

Exponent of each of the terms : 3, 8.

Terms with highest exponent : 3m³n⁵.

Therefore, degree of the polynomial is 8.

15. Answer :

The terms of the given polynomial are a³b², a²b³, -a⁴, b⁴ and 3.

Exponent of each of the terms : 5, 5, 4, 4. 0.

Terms with highest exponent : a³b², a²b³.

Therefore, degree of the polynomial is 5.

16. Answer :

= (2x² + 5xy + 9y²) + (-3x² - 5xy + 4y²)

= 2x² + 5xy + 9y² - 3x² - 5xy + 4y²

Group like terms together.

= (2x² - 3x²) + (5xy - 5xy) + (9y² + 4y²)

= -x² + 0 + 13y²

= -x² + 13y²

Thus, the degree of the polynomial is 2.

17. Answer :

= (2p⁴ - 2p³ - 4p + 5) - (p⁴ - p² + 2p + 3)

Distributive the negative sign.

= 2p⁴ - 2p³ - 4p + 5 - p⁴ + p² - 2p - 3

Group like terms together.

= (2p⁴ - p⁴) + 2p³ + p² + (-4p - 2p) + (5 - 3)

Combine like terms.

= p⁴ + 2p³ + p² + (-6p) + 2

= p⁴ + 2p³ + p² - 6p + 2

Hence, the degree of the polynomial is 4.

18. Answer :

= (3y² - 5z) - (y - 7z²) - (5y² - 6z²) + (3y + z)

= 3y² - 5z - y + 7z² - 5y² + 6z² + 3y + z

Group like terms together.

= (3y² - 5y²) + (7z² + 6z²) + (-y + 3y) + (-5z + z)

Combine like terms.

= -2y² + 13z² + 2y + (-3z)

= -2y² + 13z² + 2y - 3z

Hence, the degree of the polynomial is 2.

19. Answer :

x² + 5

20. Answer :

(2xy - 7) or (x² + y²) or (x² - 2y) or (x + 3y²)

21. Answer :

y² + 2y + 3

22. Answer :

k⁵ + k² - 1

23. Answer :

z⁴ - 3z³ + 2z

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.