Worksheet: Zeros of Polynomial Functions

In this worksheet, we will practice finding the set of zeros of a quadratic, a cubic, or a higher-degree polynomial function.

Q1:

Find, by factoring, the zeros of the function 𝑓 ( 𝑥 ) = 𝑥 + 2 𝑥 3 5 2 .

  • A 7 , 5
  • B 5 , 7
  • C 5 , 7
  • D 7 , 5
  • E 6 , 8

Q2:

What are the zeros of the function 𝑓 ( 𝑥 ) = 2 ( 𝑥 1 ) 7 2 ?

  • A 1 + 7 2 and 1 7 2
  • B 1 + 7 2 and 1 7 2
  • C 1 + 7 2 and 1 7 2
  • D 1 + 7 2 and 1 7 2
  • E 1 7 2 and 1 7 2

Q3:

Find, by factoring, the zeros of the function 𝑓 ( 𝑦 ) = 𝑦 + 8 𝑦 + 7 2 .

  • A 7 , 1
  • B 7 , 1
  • C 1 , 8
  • D 7 , 1
  • E 8 , 1

Q4:

Find the set of zeros of the function 𝑓 ( 𝑥 ) = 𝑥 1 7 𝑥 + 1 6 4 2 .

  • A { 1 }
  • B { 1 , 4 }
  • C { 4 }
  • D { 4 , 1 , 1 , 4 }
  • E { 4 , 1 }

Q5:

If the set of zeros of the function 𝑓 ( 𝑥 ) = 𝑥 + 𝑏 𝑥 + 3 4 3 2 3 is { 8 , 8 } , find the value of 𝑏 .

Q6:

Find, by factoring, the zeros of the function 𝑓 ( 𝑥 ) = 9 𝑥 + 9 𝑥 4 0 2 .

  • A 5 3 , 8 3
  • B 5 3 , 8 3
  • C 5 , 8
  • D 5 3 , 8 3
  • E 5 , 8

Q7:

Find the set of zeros of the function 𝑓 ( 𝑥 ) = 𝑥 𝑥 8 1 2 𝑥 8 1 2 2 .

  • A { 2 , 9 }
  • B { 9 , 2 , 9 }
  • C { 2 , 9 }
  • D { 9 , 2 , 9 }
  • E { 9 , 9 }

Q8:

Find the set of zeros of the function 𝑓 ( 𝑥 ) = 1 3 ( 𝑥 4 ) .

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

Q9:

Find the set of zeros of the function 𝑓 ( 𝑥 ) = 𝑥 1 𝑥 4 2 .

  • A { 2 , 1 , 2 }
  • B { 2 , 2 }
  • C { 1 }
  • D { 1 }
  • E { 2 , 2 }

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