Worksheet: Polynomial Inequalities

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


Solve the inequality 𝑥5𝑥+6𝑥<0.

  • A2<𝑥<6
  • B0<𝑥<6
  • C2<𝑥<3
  • D5<𝑥<6
  • E0<𝑥<2


Consider the graph.

Find the interval which contains all the values of 𝑥 that satisfy the inequality 𝑥+3𝑥6𝑥8<0.

  • A(4,1)(2,)
  • B(,2)
  • C(,4)(1,2)
  • D(,)
  • E(0,2)


Find the values of 𝑥 which satisfy the inequality 𝑥4𝑥+3>0.

  • A[3,1]
  • B[1,3]
  • C(1,3)
  • D[1,3]
  • E[3,1]


Solve the inequality 𝑥1440.

  • A(,12]
  • B(12,12)
  • C[12,12]
  • D[12,)
  • E(12,12)


Solve the inequality 2(𝑥+1)(𝑥+3)(𝑥6)<0.

  • A𝑥(1,3)(6,)
  • B𝑥(3,1)
  • C𝑥(6,)
  • D𝑥(,6)(3,1)
  • E𝑥(3,1)(6,)


Solve the inequality (𝑥+1)(𝑥9)0.

  • A[1,9]
  • B(1,9)
  • C(1,)
  • D[9,)
  • E[1,)


Solve the inequality 2𝑥+3𝑥20.

  • A2,12
  • B2,12
  • C12,2
  • D2,12
  • E2,12


Solve the inequality 4𝑥+3>𝑥.

  • A(1,3)
  • B[1,3]
  • C(1,3)
  • D[1,3]
  • E[3,1]


Given that 𝑓(𝑥)=𝑥3𝑥6𝑥+8 is zero when 𝑥=1, determine the conditions on 𝑥 so that 𝑓(𝑥)10.

  • A𝑥6 or 6𝑥4
  • B6𝑥6 or 𝑥3
  • C6𝑥3
  • D𝑥6 or 𝑥3
  • E𝑥6 or 𝑥3


Given that the function 𝑓(𝑥)=𝑥3𝑥6𝑥+8 has a zero at 𝑥=4, determine all 𝑥 for which the graph 𝑦=𝑓(𝑥) is below the 𝑥-axis.

  • A𝑥<2 or 1<𝑥<4
  • B𝑥<1 or 𝑥>4
  • C𝑥<2 or 𝑥>4
  • D2<𝑥<1 or 𝑥>4
  • E𝑥<2 or 𝑥>1

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