Lesson Worksheet: Degree and Coefficient of Polynomials Mathematics

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 𝑦7𝑦.

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

Q2:

Determine the coefficient and the degree of 7𝑥.

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

Q3:

If the degree of 3𝑥 is the same as that of 𝑧, what is the value of 𝑛?

Q4:

What is the degree of the expression 7𝑥12𝑥+2?

Q5:

How many terms are in the expression 4𝑥𝑦+27?

  • AOne
  • BTwo
  • CFour
  • DNone
  • EThree

Q6:

If the degree of 7𝑥 is the same as that of 6𝑦, what is the value of 𝑛?

Q7:

What is the constant term in the expression 4𝑥𝑦+27?

Q8:

What is the constant term in the expression 3𝑝+2𝑞𝑤19?

Q9:

Are 𝑎 and 4𝑎 like terms?

  • ANo
  • BYes

Q10:

How many terms are in the expression 2𝑥𝑧+𝑥𝑦𝑧9𝑥𝑦3?

Q11:

Complete the following table.

Algebraic ExpressionsVariablesNumbersOperations
6𝑤7𝑦+16𝑠???
  • Avariables: 𝑤, 𝑦, 𝑠, numbers: 6, 7, 16, operations: subtraction, addition
  • Bvariables: 𝑤, 𝑦, 𝑠, numbers: 6, 7, 16, operations: multiplication, subtraction, addition
  • Cvariables: 6, 7, 16, numbers: 𝑤, 𝑦, 𝑠, operations: multiplication, subtraction, addition
  • Dvariables: 6, 7, 16, numbers: 𝑤, 𝑦, 𝑠, operations: subtraction, addition
  • Evariables: 𝑤, 𝑦, 𝑠, numbers: 6, 7, 16, operations: multiplication, addition

Q12:

What is the constant in the expression 6𝑥+2𝑦+𝑥?

Q13:

What is the constant in the expression 6𝑥+2𝑦+𝑥+4?

Q14:

How many terms are there in 4.9𝑥?

Q15:

What terminology do we use to describe the 5 in the expression 9𝑦+5?

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

Q16:

What do we call 8𝑎 in the expression 8𝑎+3𝑥+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 𝑐, and let the number of dogs be 𝑑. The total number of tins of food required every day at the center is represented by the equation 𝑇=2𝑐+3𝑑.

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

  • A3𝑑
  • B𝑇
  • C2𝑐

Q18:

What is the variable in the expression 6𝑥+80?

  • A80
  • B6
  • C𝑥

Q19:

How many terms are there in 𝑚+36?

Q20:

What does the expression 2𝑎𝑏+3𝑐𝑑 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

Q21:

Choose the answer that makes the following statement true: The expression (𝑥+𝑦+𝑧)(𝑎+𝑏+𝑐) consists of factors, and each factor consists of terms.

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

Q22:

What does the expression 2𝑚+3𝑛 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

Q23:

What does the expression 𝑎𝑏+𝑐𝑑𝑒𝑓 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

Q24:

What does the expression 3𝑎+5𝑏+6𝑐+12𝑑 consist of?

  • A3 terms of 1 factors
  • B4 terms of 2 factors
  • C2 terms of 3 factors
  • D2 terms of 4 factors
  • E4 terms of 1 factors

Q25:

The expression 𝑥𝑦+𝑎𝑏 consists of terms and each term consists of factors.

  • A4, 2
  • B3, 2
  • C2, 4
  • D2, 3
  • E2, 2

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