Worksheet: Dividing Polynomials by Monomials

In this worksheet, we will practice dividing polynomials by monomials.

Q1:

Find the quotient of 2 1 𝑎 𝑏 7 𝑎 𝑏 .

  • A 3 𝑎
  • B 3 𝑎 𝑏
  • C 3 𝑎 𝑏
  • D 3 𝑎
  • E 3 𝑎 𝑏

Q2:

Simplify 4 3 𝑥 + 1 2 𝑥 6 𝑥 𝑥 .

  • A 4 3 𝑥 + 1 2 𝑥 + 6 𝑥
  • B 4 3 𝑥 1 2 𝑥 6 𝑥
  • C 4 3 𝑥 + 1 2 𝑥 6 𝑥
  • D 4 3 𝑥 + 1 2 𝑥 6 𝑥
  • E 4 3 𝑥 + 1 2 𝑥 6 𝑥

Q3:

Find the quotient of 2 6 𝑎 𝑏 9 𝑎 𝑏 𝑎 𝑏 .

  • A 2 6 𝑎 𝑏 9 𝑎 𝑏
  • B 2 6 𝑎 𝑏 + 9 𝑎 𝑏
  • C 2 6 𝑎 𝑏 9 𝑎 𝑏
  • D 2 6 𝑎 𝑏 9 𝑎 𝑏

Q4:

Simplify 2 3 𝑥 𝑦 + 4 9 𝑥 𝑦 + 4 1 𝑥 𝑦 𝑥 𝑦 .

  • A 2 3 𝑥 𝑦 4 9 𝑥 𝑦 + 4 1 𝑥 𝑦
  • B 2 3 𝑥 𝑦 + 4 9 𝑥 𝑦 4 1 𝑥 𝑦
  • C 2 3 𝑥 𝑦 4 9 𝑥 𝑦 4 1 𝑥 𝑦
  • D 2 3 𝑥 𝑦 4 9 𝑥 𝑦 4 1 𝑥 𝑦
  • E 2 3 𝑥 𝑦 4 9 𝑥 𝑦 4 1 𝑥 𝑦

Q5:

Simplify 1 4 4 𝑥 + 1 6 8 𝑥 + 8 4 𝑥 1 2 𝑥 + 3 𝑥 + 1 9 𝑥 + 1 8 .

  • A 1 5 𝑥 + 3 3 𝑥 + 2 5
  • B 9 𝑥 + 5 𝑥 + 1 1
  • C 9 𝑥 + 5 𝑥 + 1 1
  • D 1 5 𝑥 + 3 3 𝑥 + 2 5

Q6:

What is the height of a cuboid whose volume is 1 7 𝑥 6 𝑥 𝑦 cm3 and whose base is a square of side 𝑥 cm?

  • A 1 7 𝑥 6 cm
  • B 1 7 𝑥 6 𝑥 𝑦 cm
  • C 1 7 𝑥 6 𝑥 𝑦 cm
  • D 1 7 𝑥 6 𝑦 cm
  • E 1 7 𝑥 6 𝑥 𝑦 cm

Q7:

Simplify 1 2 𝑎 1 1 𝑎 𝑏 1 2 𝑎 𝑏 2 𝑎 𝑏 .

  • A 1 3 0 𝑎 𝑏 1 4 2 𝑎 𝑏
  • B 6 6 𝑎 𝑏 7 2 𝑎 𝑏
  • C 1 3 0 𝑎 𝑏 1 4 2 𝑎 𝑏
  • D 6 6 𝑎 𝑏 7 2 𝑎 𝑏

Q8:

Given that 17 tennis balls of radius 𝑟 c m can fit into a box whose dimensions are 2 𝑟 c m , 2 𝑟 c m , and 5 1 𝑟 c m , what is the ratio between the volume of the balls and the volume of the box?

  • A 𝜋
  • B 1 3 𝜋
  • C 1 9
  • D 1 9 𝜋
  • E 1 3

Q9:

What is the length of a rectangle whose area is 7 𝑥 𝑦 + 2 4 𝑥 𝑦 + 1 6 𝑥 𝑦 cm2 and whose width is 𝑥 𝑦 cm?

  • A 7 𝑥 𝑦 + 2 4 𝑥 𝑦 1 6 𝑥 𝑦 cm
  • B 7 𝑥 𝑦 2 4 𝑥 𝑦 + 1 6 𝑥 𝑦 cm
  • C 7 𝑥 𝑦 + 2 4 𝑥 𝑦 + 1 6 𝑥 𝑦 cm
  • D 7 𝑥 𝑦 + 2 4 𝑥 𝑦 + 1 6 𝑥 𝑦 cm

Q10:

The area of a triangle is 1 2 𝑥 + 4 𝑥 cm2, and its base is 4 𝑥 m. Write an expression for its height.

  • A 4 8 𝑥 + 1 6 𝑥 cm
  • B ( 1 2 𝑥 + 4 ) cm
  • C ( 3 𝑥 + 1 ) cm
  • D ( 6 𝑥 + 2 ) cm

Q11:

The area of the shaded region in the figure below is 3 𝑥 𝑦 + 1 0 𝑥 𝑦 cm2. By considering the areas of the rectangles 𝐴 𝐵 𝐶 𝐷 and 𝑀 𝐸 𝑁 𝐹 , find the length of 𝐹 𝑁 .

  • A ( 9 𝑥 𝑦 + 8 6 ) cm
  • B ( 3 𝑥 𝑦 + 3 8 ) cm
  • C ( 9 𝑥 𝑦 + 3 8 ) cm
  • D ( 3 𝑥 𝑦 + 8 6 ) cm
  • E ( 3 𝑥 𝑦 + 5 8 ) cm

Q12:

Expand and simplify 2 𝑎 3 7 𝑏 5 𝑎 3 8 𝑏 .

  • A 1 0 𝑎 9 1 6 𝑎 𝑏 3 + 5 6 𝑏
  • B 1 0 𝑎 9 1 7 𝑎 𝑏 7 𝑏
  • C 1 0 𝑎 9 3 5 𝑎 𝑏 3 + 5 6 𝑏
  • D 1 0 𝑎 9 1 7 𝑎 𝑏 + 5 6 𝑏
  • E 1 0 𝑎 9 1 9 𝑎 𝑏 3 5 6 𝑏

Q13:

Expand and simplify ( 4 𝑥 + 𝑦 ) .

  • A 1 6 𝑥 + 3 6 𝑥 𝑦 + 1 2 𝑥 𝑦 + 𝑦
  • B 6 4 𝑥 + 3 2 𝑥 𝑦 + 8 𝑥 𝑦 + 𝑦
  • C 6 4 𝑥 + 1 6 𝑥 𝑦 + 4 𝑥 𝑦 + 𝑦
  • D 6 4 𝑥 + 4 8 𝑥 𝑦 + 1 2 𝑥 𝑦 + 𝑦
  • E 6 4 𝑥 + 𝑦

Q14:

Find the quotient of 1 6 𝑎 𝑏 2 𝑎 𝑏 .

  • A 8 𝑎 𝑏
  • B 8 𝑎 𝑏
  • C 8 𝑎 𝑏
  • D 8 𝑎 𝑏
  • E 8 𝑎 𝑏

Q15:

What is the length of a rectangle whose area is 2 1 𝑥 𝑦 + 2 3 𝑥 𝑦 + 2 0 𝑥 𝑦 cm2 and whose width is 𝑥 𝑦 cm?

  • A 2 1 𝑥 𝑦 + 2 3 𝑥 𝑦 2 0 𝑥 𝑦 cm
  • B 2 1 𝑥 𝑦 2 3 𝑥 𝑦 + 2 0 𝑥 𝑦 cm
  • C 2 1 𝑥 𝑦 + 2 3 𝑥 𝑦 + 2 0 𝑥 𝑦 cm
  • D 2 1 𝑥 𝑦 + 2 3 𝑥 𝑦 + 2 0 𝑥 𝑦 cm

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