Lesson Worksheet: Polynomial Equations Mathematics

In this worksheet, we will practice using different strategies for solving polynomial equations of degree greater than two.

Q1:

Solve the equation (3𝑥1)(5𝑥+6)(3𝑥4)(8𝑥+7)=0.

  • A𝑥=1, 𝑥=6, 𝑥=4, 𝑥=7
  • B𝑥=13, 𝑥=65, 𝑥=43, 𝑥=78
  • C𝑥=13, 𝑥=65, 𝑥=43, 𝑥=78
  • D𝑥=3, 𝑥=56, 𝑥=34, 𝑥=87
  • E𝑥=1, 𝑥=6, 𝑥=4, 𝑥=7

Q2:

By factoring, find all the solutions to 𝑥+2𝑥17𝑥18𝑥+72=0, given that (𝑥3) and (𝑥+4) are factors of 𝑥+2𝑥17𝑥18𝑥+72.

  • A𝑥=3, 𝑥=4, 𝑥=2, 𝑥=3
  • B𝑥=3, 𝑥=4, 𝑥=2, 𝑥=3
  • C𝑥=3, 𝑥=4, 𝑥=2, 𝑥=3
  • D𝑥=3, 𝑥=4, 𝑥=2
  • E𝑥=3, 𝑥=4, 𝑥=2, 𝑥=3

Q3:

Solve the equation (𝑥1)(𝑥+6)(𝑥4)(𝑥+7)=0.

  • A𝑥=1, 𝑥=6, 𝑥=4, 𝑥=7
  • B𝑥=1, 𝑥=6, 𝑥=4, 𝑥=7
  • C𝑥=1, 𝑥=6, 𝑥=4, 𝑥=7
  • D𝑥=1, 𝑥=6, 𝑥=4, 𝑥=7
  • E𝑥=1, 𝑥=6, 𝑥=4, 𝑥=7

Q4:

Given that 𝑥 is in , find the value of 𝑥 which satisfies the following equation 3𝑥6𝑥+9=0. Give your answer to the nearest hundredth.

  • A𝑥=1.26, 𝑥=3.00 or 𝑥=3.00
  • B𝑥=1.41
  • C𝑥=1.26
  • D𝑥=1.26 or 𝑥=3.00

Q5:

Find the solution set of the equation 𝑥506𝑥58=0 in .

  • A58,506
  • B58,506
  • C58,58,506
  • D506,506,58
  • E58,58,506

Q6:

Michael needs to produce lidless square-based boxes with a height of 4 inches and a volume of 320 cubic inches. He uses the net as seen in the given figure but needs to work out the value of 𝑥. Find 𝑥, giving your solution to two decimal places.

Q7:

An engineering company makes some aluminum cubes for a customer. Each cube has a surface area of 𝑥 cm2 and a volume of 𝑥 cm3. What is the length of the side of each cube?

Q8:

A customer has placed an order for some precision-engineered cubes, but part of the order form was destroyed in a paint-spilling accident. The only information we have is that each cube has a surface area of 𝑥 cm2 and a volume of (2𝑥) cm3. What is the length of the side of each cube?

Q9:

A solid metal cuboid whose dimensions are 2𝑥 cm, 6𝑥 cm, and 10𝑥 cm, was melted and made into small cubes. If the edges of the small cubes are 2𝑥 cm, how many can be made from the melted cuboid?

Q10:

Given that 𝑦+1𝑦=79, find 𝑦+1𝑦.

  • A8
  • B8,8
  • C9,9
  • D9
  • E81

Q11:

Find the solution set of 2𝑥+2=0 in .

  • A
  • B{1,1}
  • C{1,0}
  • D{1}

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