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‘ฆ โˆ’ 7 ๐‘ฆ 4 2 .

  • Asecond degree
  • Bfirst degree
  • Cthird degree
  • Dfourth degree

Q2:

Determine the coefficient and the degree of โˆ’ 7 ๐‘ฅ ๏Šฉ .

  • Acoefficient = โˆ’ 2 1 , degree = 3
  • Bcoefficient = 3 , degree = โˆ’ 7
  • Ccoefficient = โˆ’ 7 , degree = โˆ’ 2 1
  • Dcoefficient = โˆ’ 7 , degree = 3
  • Ecoefficient = 0 , degree = 3

Q3:

If the degree of โˆ’ 3 ๐‘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 7 ๐‘ฅ โˆ’ 1 2 ๐‘ฅ + 2 2 ?

Q5:

How many terms are in the expression 4 ๐‘ฅ โˆ’ ๐‘ฆ + 2 7 2 ?

  • A One
  • B Two
  • C None
  • D Three
  • EFour

Q6:

If the degree of 7 ๐‘ฅ ๏Šซ is the same as that of โˆ’ 6 ๐‘ฆ ๏Š , what is the value of ๐‘› ?

Q7:

What is the constant term in the expression 4 ๐‘ฅ โˆ’ ๐‘ฆ + 2 7 2 ?

Q8:

What is the constant term in the expression 3 ๐‘ + 2 ๐‘ž โˆ’ ๐‘ค โˆ’ 1 9 2 2 ?

Q9:

Are ๐‘Ž ๏Šช and 4 ๐‘Ž like terms?

  • Ano
  • Byes

Q10:

How many terms are in the expression 2 ๐‘ฅ ๐‘ง + ๐‘ฅ ๐‘ฆ ๐‘ง โˆ’ 9 ๐‘ฅ ๐‘ฆ โˆ’ 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: multiplication, addition
  • Bvariables: ๐‘ค , ๐‘ฆ , ๐‘  , numbers: 6, 7, 16, operations: subtraction, addition
  • Cvariables: 6, 7, 16, numbers: ๐‘ค , ๐‘ฆ , ๐‘  , operations: multiplication, subtraction, addition
  • Dvariables: ๐‘ค , ๐‘ฆ , ๐‘  , numbers: 6, 7, 16, operations: multiplication, subtraction, addition
  • Evariables: 6, 7, 16, numbers: ๐‘ค , ๐‘ฆ , ๐‘  , operations: subtraction, addition

Q12:

What is the constant in the expression 6 ๐‘ฅ + 2 ๐‘ฆ + ๐‘ฅ 3 ?

Q13:

What is the constant in the expression 6 ๐‘ฅ + 2 ๐‘ฆ + ๐‘ฅ + 4 3 ?

Q14:

How many terms are there in 4 . 9 ๐‘ฅ 2 ?

Q15:

What terminology do we use to describe the 5 in the expression 9 ๐‘ฆ + 5 ?

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

Q16:

What do we call 8 ๐‘Ž in the expression 8 ๐‘Ž + 3 ๐‘ฅ + 4 ?

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

Q17:

An animal shelter cares for cats and dogs. All of the animals at the centre 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 centre be ๐‘ , and let the number of dogs be ๐‘‘ . The total number of cans of food required every day at the centre is represented by the equation

Which term represents the number of cans 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
  • Bvariables: ๐‘‘ , ๐‘ , numbers: 14, 11, operations: addition
  • Cvariables: 14, 11, numbers: ๐‘‘ , ๐‘ , operations: multiplication, addition
  • Dvariables: ๐‘‘ , ๐‘ , numbers: 14, 11, operations: multiplication, addition
  • Evariables: 14, 11, numbers: ๐‘‘ , ๐‘ , 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, addition, subtraction
  • BVariables: ๐‘ฅ , ๐‘ฆ , ๐‘š , Numbers: 9, 4, 3, 16, Operations: division, addition, subtraction
  • CVariables: 9, 4, 3, 16, Numbers: ๐‘ฅ , ๐‘ฆ , ๐‘š , Operations: multiplication, division, addition, subtraction
  • DVariables: ๐‘ฅ , ๐‘ฆ , ๐‘š , Numbers: 9, 4, 3, 16, Operations: multiplication, division, addition, subtraction
  • EVariables: 9, 4, 3, 16, Numbers: ๐‘ฅ , ๐‘ฆ , ๐‘š , Operations: division, addition, subtraction

Q20:

What is the variable in the expression 6 ๐‘ฅ + 8 0 ?

  • A6
  • B80
  • C ๐‘ฅ

Q21:

How many terms are there in ๐‘š + 3 6 ?

Q22:

What does the expression 2 ๐‘Ž ๐‘ + 3 ๐‘ ๐‘‘ consist of?

  • A3 terms of 1 factors
  • B3 terms of 2 factors
  • C2 terms of 1 factors
  • D2 terms of 3 factors
  • E2 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
  • B3, 2
  • C3, 6
  • D2, 3
  • E3, 3

Q24:

What does the expression 2 ๐‘š + 3 ๐‘› consist of?

  • A1 terms of 1 factors
  • B2 terms of 3 factors
  • C2 terms of 1 factors
  • D2 terms of 2 factors
  • E1 terms of 2 factors

Q25:

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

  • A3 terms of 1 factors
  • B2 terms of 3 factors
  • C2 terms of 1 factors
  • D3 terms of 2 factors
  • E2 terms of 2 factors

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