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

Q1:

Consider the polynomial function 𝑓 ( π‘₯ ) = βˆ’ 8 π‘₯ + 3 π‘₯ βˆ’ 1 2 π‘₯ + 5 π‘₯ βˆ’ 1 2 5 4 6 2 .

What is its degree?

What is its leading coefficient?

Q2:

What is the degree of the equation ( π‘₯ + 1 1 ) ( π‘₯ βˆ’ 1 1 ) = 0 ?

  • Afourth
  • Bfirst
  • Cthird
  • Dsecond

Q3:

Find all the possible values for 𝑛 which make the function 𝑓 ( π‘₯ ) = 𝑛 π‘₯ + 5 π‘₯ + 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 ( π‘₯ ) = π‘₯ ο€Ή π‘₯ + π‘₯  βˆ’ π‘₯ ο€Ή π‘₯ βˆ’ 6 π‘₯  2 5 3 3 4 .

  • A6
  • B3
  • C5
  • D7

Q5:

Determine the coefficient and the degree of 6 π‘₯ 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

Q6:

Consider the polynomial function 𝑓 ( π‘₯ ) = βˆ’ 3 π‘₯ ( 4 π‘₯ + 2 π‘₯ ) βˆ’ 2 π‘₯ ( βˆ’ π‘₯ + π‘₯ ) ( βˆ’ 2 π‘₯ + 7 π‘₯ ) 2 7 5 3 2 4 5 .

What is its degree?

What is its leading coefficient?

Q7:

Find the degree of the function 𝑓 ( π‘₯ ) = βˆ’ 2 π‘₯ ο€Ή βˆ’ 6 π‘₯ βˆ’ 5 π‘₯  3 2 .