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Worksheet: Solving Nonlinear Polynomial Inequalities

Q1:

Find all solutions to the inequality . Write your answer as an interval.

  • A
  • B
  • C
  • D
  • E

Q2:

Find all solutions to the inequality . Write your answer as an interval.

  • A
  • B
  • C
  • D
  • E

Q3:

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

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

Q4:

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

  • A π‘₯ < βˆ’ 2 or π‘₯ > 4
  • B βˆ’ 2 < π‘₯ < 1 or π‘₯ > 4
  • C π‘₯ < βˆ’ 2 or π‘₯ > 1
  • D π‘₯ < βˆ’ 2 or 1 < π‘₯ < 4
  • E π‘₯ < 1 or π‘₯ > 4

Q5:

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

  • A ( βˆ’ 4 , 5 )
  • B [ βˆ’ 4 , 5 ]
  • C ( βˆ’ ∞ , βˆ’ 4 ) βˆͺ ( 5 , + ∞ )
  • D ( βˆ’ 4 , 0 ) βˆͺ ( 0 , 5 )