Worksheet: Polynomial Inequalities

In this worksheet, we will practice solving polynomial inequalities using factoring, end behavior, and sign charts.

Q1:

Find all solutions to the inequality ( 𝑥 + 4 ) < 1 3 6 9 ( 𝑥 + 4 ) 2 . Write your answer as an interval.

  • A ] 2 1 , 4 [
  • B [ 1 2 , 1 3 ]
  • C ] 1 2 , 1 3 [
  • D ] 2 1 , 4 [
  • E [ 2 1 , 4 ]

Q2:

Given that is zero when , determine the conditions on so that .

  • A
  • B or
  • C or
  • D or
  • E or

Q3:

Given that the function 𝑓 ( 𝑥 ) = 𝑥 3 𝑥 6 𝑥 + 8 3 2 has a zero at 𝑥 = 4 , determine all 𝑥 for which the graph 𝑦 = 𝑓 ( 𝑥 ) is below the 𝑥 -axis.

  • A 𝑥 < 2 or 𝑥 > 4
  • B 2 < 𝑥 < 1 or 𝑥 > 4
  • C 𝑥 < 2 or 𝑥 > 1
  • D 𝑥 < 2 or 1 < 𝑥 < 4
  • E 𝑥 < 1 or 𝑥 > 4

Q4:

Solve the inequality 𝑝 𝑝 2 0 𝑝 < 0 4 3 2 .

  • A ( 4 , 5 )
  • B [ 4 , 5 ]
  • C ( , 4 ) ( 5 , + )
  • D ( 4 , 0 ) ( 0 , 5 )

Q5:

Find all solutions to the inequality ( 𝑥 + 2 ) < 1 7 6 5 ( 𝑥 + 2 ) 2 . Write your answer as an interval.

  • A ] 1 8 , 9 [
  • B [ 1 3 , 1 4 ]
  • C ] 1 3 , 1 4 [
  • D ] 1 8 , 9 [
  • E [ 1 8 , 9 ]

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.