Worksheet: Degree and Leading Coefficient of a One-Variable Polynomial

In this worksheet, we will practice stating the degree and leading coefficient of one-variable polynomials.

Q1:

Consider the polynomial function 𝑓 ( 𝑥 ) = 8 𝑥 + 3 𝑥 1 2 𝑥 + 5 𝑥 1 2 5 4 6 2 .

What is its degree?

What is its leading coefficient?

Q2:

Consider the polynomial function 𝑓 ( 𝑥 ) = 3 𝑥 ( 4 𝑥 + 2 𝑥 ) 2 𝑥 ( 𝑥 + 𝑥 ) ( 2 𝑥 + 7 𝑥 ) 2 7 5 3 2 4 5 .

What is its degree?

What is its leading coefficient?

Q3:

Find all the possible values for 𝑛 which make the function 𝑓 ( 𝑥 ) = 𝑛 𝑥 + 5 𝑥 + 1 7 4 𝑛 a fourth degree polynomial.

  • A { 4 , 3 , 2 }
  • B { 4 , 3 }
  • C { 3 , 2 , 1 }
  • D { 4 , 3 , 2 , 1 }

Q4:

Find the degree of the polynomial 𝑓 ( 𝑥 ) = 𝑥 𝑥 + 𝑥 𝑥 𝑥 6 𝑥 2 5 3 3 4 .

  • A6
  • B3
  • C5
  • D7

Q5:

Find the degree of the function 𝑓 ( 𝑥 ) = 2 𝑥 6 𝑥 5 𝑥 3 2 .

Q6:

Determine the coefficient and the degree of 6 𝑥 𝑦 𝑧 2 5 5 .

  • Acoefficient = 6 , degree = 5
  • Bcoefficient = 2 , degree = 5
  • Ccoefficient = 2 , degree = 1 2
  • Dcoefficient = 6 , degree = 1 2
  • Ecoefficient = 0 , degree = 5

Q7:

What is the degree of the equation ( 𝑥 + 1 1 ) ( 𝑥 1 1 ) = 0 ?

  • Afourth
  • Bfirst
  • Cthird
  • Dsecond

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