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 (3𝑥1)(5𝑥+6)(3𝑥4)(8𝑥+7)=0.

  • A 𝑥 = 1 , 𝑥 = 6 , 𝑥 = 4 , 𝑥 = 7
  • B 𝑥 = 1 3 , 𝑥 = 6 5 , 𝑥 = 4 3 , 𝑥 = 7 8
  • C 𝑥 = 1 3 , 𝑥 = 6 5 , 𝑥 = 4 3 , 𝑥 = 7 8
  • D 𝑥 = 3 , 𝑥 = 5 6 , 𝑥 = 3 4 , 𝑥 = 8 7
  • E 𝑥 = 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.

  • A 𝑥 = 3 , 𝑥 = 4 , 𝑥 = 2 , 𝑥 = 3
  • B 𝑥 = 3 , 𝑥 = 4 , 𝑥 = 2 , 𝑥 = 3
  • C 𝑥 = 3 , 𝑥 = 4 , 𝑥 = 2 , 𝑥 = 3
  • D 𝑥 = 3 , 𝑥 = 4 , 𝑥 = 2
  • E 𝑥 = 3 , 𝑥 = 4 , 𝑥 = 2 , 𝑥 = 3

Q3:

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

  • A 𝑥 = 1 , 𝑥 = 6 , 𝑥 = 4 , 𝑥 = 7
  • B 𝑥 = 1 , 𝑥 = 6 , 𝑥 = 4 , 𝑥 = 7
  • C 𝑥 = 1 , 𝑥 = 6 , 𝑥 = 4 , 𝑥 = 7
  • D 𝑥 = 1 , 𝑥 = 6 , 𝑥 = 4 , 𝑥 = 7
  • E 𝑥 = 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.

  • A 𝑥 = 1 . 2 6 , 𝑥 = 3 . 0 0 or 𝑥=3.00
  • B 𝑥 = 1 . 4 1
  • C 𝑥 = 1 . 2 6
  • D 𝑥 = 1 . 2 6 or 𝑥=3.00

Q5:

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

  • A 5 8 , 5 0 6
  • B 5 8 , 5 0 6
  • C 5 8 , 5 8 , 5 0 6
  • D 5 0 6 , 5 0 6 , 5 8
  • E 5 8 , 5 8 , 5 0 6

Q6:

According to the fundamental theorem of algebra, how many complex solutions does the equation 𝑥+3𝑥3𝑥+2=0 have, counted with multiplicity?

  • AEight
  • BExactly two
  • CInfinitely many
  • DAt least one, but the exact number is unknown.

Q7:

Find the dimensions of the box described: the length is 3 inches longer than the width, the width is 2 inches longer than the height, and the volume is 120 cubic inches.

  • A6 in by 8 in by 9 in
  • B4 in by 6 in by 9 in
  • C5 in by 10 in by 15 in
  • D3 in by 5 in by 8 in
  • E5 in by 7 in by 8 in

Q8:

Find the dimensions of a box with a length three times its height, a height 1 inch less than its width, and a volume of 108 cubic inches.

  • A2 in by 3 in by 6 in
  • B4 in by 5 in by 12 in
  • C3 in by 4 in by 5 in
  • D3 in by 4 in by 6 in
  • E3 in by 4 in by 9 in

Q9:

Find the dimensions of the box whose length is twice the width, height is 2 inches greater than the width, and volume is 192 cubic inches.

  • A2 in by 4 in by 6 in
  • B2 in by 4 in by 8 in
  • C4 in by 6 in by 6 in
  • D4 in by 4 in by 8 in
  • E4 in by 6 in by 8 in

Q10:

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.

Q11:

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?

Q12:

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?

Q13:

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?

Q14:

Given that 𝑦+1𝑦=79, find 𝑦+1𝑦.

  • A8
  • B 8 , 8
  • C 9 , 9
  • D9
  • E81

Q15:

Find the solution set of 2𝑥+2=0 in .

  • A
  • B { 1 , 1 }
  • C { 1 , 0 }
  • D { 1 }

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