Worksheet: Polynomial Equations

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

Q1:

Solve the equation (3π‘₯βˆ’1)(5π‘₯+6)(3π‘₯βˆ’4)(8π‘₯+7)=0.

  • Aπ‘₯=βˆ’1, π‘₯=6, π‘₯=βˆ’4, π‘₯=7
  • Bπ‘₯=βˆ’13, π‘₯=65, π‘₯=βˆ’43, π‘₯=78
  • Cπ‘₯=13, π‘₯=βˆ’65, π‘₯=43, π‘₯=βˆ’78
  • Dπ‘₯=3, π‘₯=βˆ’56, π‘₯=34, π‘₯=βˆ’87
  • Eπ‘₯=1, π‘₯=βˆ’6, π‘₯=4, π‘₯=βˆ’7

Q2:

By factoring, find all the solutions to π‘₯+2π‘₯βˆ’17π‘₯βˆ’18π‘₯+72=0οŠͺ, given that (π‘₯βˆ’3) and (π‘₯+4) are factors of π‘₯+2π‘₯βˆ’17π‘₯βˆ’18π‘₯+72οŠͺ.

  • Aπ‘₯=βˆ’3, π‘₯=βˆ’4, π‘₯=βˆ’2, π‘₯=3
  • Bπ‘₯=3, π‘₯=4, π‘₯=2, π‘₯=βˆ’3
  • Cπ‘₯=3, π‘₯=βˆ’4, π‘₯=2, π‘₯=βˆ’3
  • Dπ‘₯=3, π‘₯=βˆ’4, π‘₯=βˆ’2
  • Eπ‘₯=βˆ’3, π‘₯=4, π‘₯=βˆ’2, π‘₯=3

Q3:

Solve the equation (π‘₯βˆ’1)(π‘₯+6)(π‘₯βˆ’4)(π‘₯+7)=0.

  • Aπ‘₯=1, π‘₯=6, π‘₯=4, π‘₯=7
  • Bπ‘₯=1, π‘₯=βˆ’6, π‘₯=4, π‘₯=βˆ’7
  • Cπ‘₯=1, π‘₯=βˆ’6, π‘₯=βˆ’4, π‘₯=βˆ’7
  • Dπ‘₯=βˆ’1, π‘₯=6, π‘₯=βˆ’4, π‘₯=7
  • Eπ‘₯=βˆ’1, π‘₯=βˆ’6, π‘₯=βˆ’4, π‘₯=βˆ’7

Q4:

Given that π‘₯ is in ℝ, find the value of π‘₯ which satisfies the following equation ο€Ή3π‘₯βˆ’6π‘₯+9=0. Give your answer to the nearest hundredth.

  • Aπ‘₯=1.26, π‘₯=3.00 or π‘₯=βˆ’3.00
  • Bπ‘₯=1.41
  • Cπ‘₯=1.26
  • Dπ‘₯=1.26 or π‘₯=3.00

Q5:

Find the solution set of the equation ο€Ήπ‘₯βˆ’506π‘₯βˆ’58=0 in ℝ.

  • Aο«βˆ’βˆš58,βˆ’βˆš506
  • B√58,√506
  • C√58,βˆ’βˆš58,√506
  • D√506,βˆ’βˆš506,√58
  • E√58,βˆ’βˆš58,βˆ’βˆš506

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 π‘₯. Find π‘₯, 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 π‘₯ cm2 and a volume of π‘₯ 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 π‘₯ cm2 and a volume of (2π‘₯) cm3. What is the length of the side of each cube?

Q9:

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

Q10:

Given that 𝑦+1𝑦=79, find 𝑦+1𝑦.

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

Q11:

Find the solution set of βˆ’2π‘₯+2=0οŠͺ in ℝ.

  • Aβˆ…
  • B{1,βˆ’1}
  • C{1,0}
  • D{1}

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