Worksheet: Degree and Coefficient of Polynomials

In this worksheet, we will practice determining the degree of a polynomial and using the terminology associated with polynomials, such as terms, coefficients, and constants.

Q1:

Determine the degree of ๐‘ฆโˆ’7๐‘ฆ๏Šช๏Šจ.

  • Athird degree
  • Bsecond degree
  • Cfirst degree
  • Dfourth degree

Q2:

Determine the coefficient and the degree of โˆ’7๐‘ฅ๏Šฉ.

  • Acoefficient =3, degree =โˆ’7
  • Bcoefficient =โˆ’7, degree =โˆ’21
  • Ccoefficient =0, degree =3
  • Dcoefficient =โˆ’7, degree =3
  • Ecoefficient =โˆ’21, degree =3

Q3:

If the degree of โˆ’3๐‘ฅ๏Šฉ is the same as that of ๐‘ง๏Š, what is the value of ๐‘›?

Q4:

What is the degree of the expression 7๐‘ฅโˆ’12๐‘ฅ+2๏Šจ?

Q5:

How many terms are in the expression 4๐‘ฅโˆ’๐‘ฆ+27๏Šจ?

  • AOne
  • BTwo
  • CFour
  • DNone
  • EThree

Q6:

If the degree of 7๐‘ฅ๏Šซ is the same as that of โˆ’6๐‘ฆ๏Š, what is the value of ๐‘›?

Q7:

What is the constant term in the expression 4๐‘ฅโˆ’๐‘ฆ+27๏Šจ?

Q8:

What is the constant term in the expression 3๐‘+2๐‘žโˆ’๐‘คโˆ’19๏Šจ๏Šจ?

Q9:

Are ๐‘Ž๏Šช and 4๐‘Ž like terms?

  • Ano
  • Byes

Q10:

How many terms are in the expression 2๐‘ฅ๐‘ง+๐‘ฅ๐‘ฆ๐‘งโˆ’9๐‘ฅ๐‘ฆโˆ’3๏Šจ๏Šฉ๏Šฉ๏Šซ๏Šช๏Šซ?

Q11:

Complete the following table.

Algebraic Expressions Variables Numbers Operations
6 ๐‘ค โˆ’ 7 ๐‘ฆ + 1 6 ๐‘  ? ? ?
  • Avariables: ๐‘ค, ๐‘ฆ, ๐‘ , numbers: 6, 7, 16, operations: subtraction, addition
  • Bvariables: ๐‘ค, ๐‘ฆ, ๐‘ , numbers: 6, 7, 16, operations: multiplication, subtraction, addition
  • Cvariables: 6, 7, 16, numbers: ๐‘ค, ๐‘ฆ, ๐‘ , operations: multiplication, subtraction, addition
  • Dvariables: 6, 7, 16, numbers: ๐‘ค, ๐‘ฆ, ๐‘ , operations: subtraction, addition
  • Evariables: ๐‘ค, ๐‘ฆ, ๐‘ , numbers: 6, 7, 16, operations: multiplication, addition

Q12:

What is the constant in the expression 6๐‘ฅ+2๐‘ฆ+๐‘ฅ๏Šฉ?

Q13:

What is the constant in the expression 6๐‘ฅ+2๐‘ฆ+๐‘ฅ+4๏Šฉ?

Q14:

How many terms are there in 4.9๐‘ฅ๏Šจ?

Q15:

What terminology do we use to describe the 5 in the expression 9๐‘ฆ+5?

  • Aa quotient
  • Ba factor
  • Ca variable
  • Da coefficient
  • Ea constant

Q16:

What do we call 8๐‘Ž in the expression 8๐‘Ž+3๐‘ฅ+4?

  • Aan quotient
  • Ba coefficient
  • Ca factor
  • Da term
  • Ea constant

Q17:

An animal shelter cares for cats and dogs. All of the animals at the center eat canned food. Every day, each cat eats 2 cans of food, and each dog eats 3 cans of food. Let the number of cats at the center be ๐‘, and let the number of dogs be ๐‘‘. The total number of tins of food required every day at the center is represented by the equation ๐‘‡=2๐‘+3๐‘‘.

Which term represents the number of tins of food eaten by the cats?

  • A 3 ๐‘‘
  • B ๐‘‡
  • C 2 ๐‘

Q18:

Complete the following table.

Algebraic Expressions Variables Numbers Operations
1 4 ๐‘‘ + 1 1 ๐‘ ? ? ?
  • Avariables: ๐‘‘, ๐‘, numbers: 14, 11, operations: multiplication, addition
  • Bvariables: ๐‘‘, ๐‘, numbers: 14, 11, operations: multiplication
  • Cvariables: 14, 11, numbers: ๐‘‘, ๐‘, operations: addition
  • Dvariables: 14, 11, numbers: ๐‘‘, ๐‘, operations: multiplication, addition
  • Evariables: ๐‘‘, ๐‘, numbers: 14, 11, operations: addition

Q19:

Complete the table below.

Algebraic Expression Variables Numbers Operations
9 ๐‘ฅ ๐‘ฆ รท 4 + 3 ๐‘š โˆ’ 1 6 ? ? ?
  • AVariables: ๐‘ฅ, ๐‘ฆ, ๐‘š, Numbers: 9, 4, 3, 16, Operations: multiplication, division, addition, subtraction
  • BVariables: 9, 4, 3, 16, Numbers: ๐‘ฅ, ๐‘ฆ, ๐‘š, Operations: multiplication, division, addition, subtraction
  • CVariables: ๐‘ฅ, ๐‘ฆ, ๐‘š, Numbers: 9, 4, 3, 16, Operations: multiplication, addition, subtraction
  • DVariables: 9, 4, 3, 16, Numbers: ๐‘ฅ, ๐‘ฆ, ๐‘š, Operations: division, addition, subtraction
  • EVariables: ๐‘ฅ, ๐‘ฆ, ๐‘š, Numbers: 9, 4, 3, 16, Operations: division, addition, subtraction

Q20:

What is the variable in the expression 6๐‘ฅ+80?

  • A80
  • B6
  • C ๐‘ฅ

Q21:

How many terms are there in ๐‘š+36?

Q22:

What does the expression 2๐‘Ž๐‘+3๐‘๐‘‘ consist of?

  • A2 terms of 3 factors
  • B3 terms of 1 factors
  • C2 terms of 1 factors
  • D2 terms of 2 factors
  • E3 terms of 2 factors

Q23:

Choose the answer that makes the following statement true: The expression (๐‘ฅ+๐‘ฆ+๐‘ง)(๐‘Ž+๐‘+๐‘) consists of factors, and each factor consists of terms.

  • A6, 3
  • B2, 3
  • C3, 6
  • D3, 2
  • E3, 3

Q24:

What does the expression 2๐‘š+3๐‘› consist of?

  • A2 terms of 1 factors
  • B1 terms of 2 factors
  • C1 terms of 1 factors
  • D2 terms of 2 factors
  • E2 terms of 3 factors

Q25:

What does the expression ๐‘Ž๐‘+๐‘๐‘‘โˆ’๐‘’๐‘“ consist of?

  • A2 terms of 3 factors
  • B2 terms of 1 factors
  • C3 terms of 2 factors
  • D2 terms of 2 factors
  • E3 terms of 1 factors

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