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Worksheet: Dividing Polynomials by Monomials

Q1:

Find the quotient of 2 1 π‘Ž 𝑏 7 π‘Ž 𝑏 6 .

  • A 3 π‘Ž 6
  • B 3 π‘Ž 𝑏 6
  • C 3 π‘Ž 𝑏 5
  • D 3 π‘Ž 5
  • E 3 π‘Ž 𝑏 7 2

Q2:

Find the quotient of βˆ’ 1 6 π‘Ž 𝑏 2 π‘Ž 𝑏 6 7 .

  • A βˆ’ 8 π‘Ž 𝑏 6 6
  • B βˆ’ 8 π‘Ž 𝑏 6 7
  • C βˆ’ 8 π‘Ž 𝑏 5 7
  • D βˆ’ 8 π‘Ž 𝑏 5 6
  • E βˆ’ 8 π‘Ž 𝑏 7 8

Q3:

Simplify βˆ’ 4 3 π‘₯ + 1 2 π‘₯ βˆ’ 6 π‘₯ π‘₯    .

  • A βˆ’ 4 3 π‘₯ + 1 2 π‘₯ + 6 π‘₯  
  • B βˆ’ 4 3 π‘₯ βˆ’ 1 2 π‘₯ βˆ’ 6 π‘₯  
  • C βˆ’ 4 3 π‘₯ + 1 2 π‘₯ βˆ’ 6 π‘₯  
  • D βˆ’ 4 3 π‘₯ + 1 2 π‘₯ βˆ’ 6 π‘₯  
  • E βˆ’ 4 3 π‘₯ + 1 2 π‘₯ βˆ’ 6 π‘₯   

Q4:

Find the quotient of 2 6 π‘Ž 𝑏 βˆ’ 9 π‘Ž 𝑏 π‘Ž 𝑏 7 5 3 5 2 .

  • A 2 6 π‘Ž 𝑏 βˆ’ 9 π‘Ž 𝑏 5 5 5
  • B 2 6 π‘Ž 𝑏 + 9 π‘Ž 𝑏 5 4 4
  • C 2 6 π‘Ž 𝑏 βˆ’ 9 π‘Ž 𝑏 5 4 5 4
  • D 2 6 π‘Ž 𝑏 βˆ’ 9 π‘Ž 𝑏 5 4 4

Q5:

Simplify 2 3 π‘₯ 𝑦 + 4 9 π‘₯ 𝑦 + 4 1 π‘₯ 𝑦 βˆ’ π‘₯ 𝑦 5 3 4 3 3 3 .

  • A βˆ’ 2 3 π‘₯ 𝑦 βˆ’ 4 9 π‘₯ 𝑦 + 4 1 π‘₯ 𝑦 4 2 3 2 2 2
  • B βˆ’ 2 3 π‘₯ 𝑦 + 4 9 π‘₯ 𝑦 βˆ’ 4 1 π‘₯ 𝑦 4 2 3 2 2 2
  • C βˆ’ 2 3 π‘₯ 𝑦 βˆ’ 4 9 π‘₯ 𝑦 βˆ’ 4 1 π‘₯ 𝑦 4 3 3 3 2 3
  • D βˆ’ 2 3 π‘₯ 𝑦 βˆ’ 4 9 π‘₯ 𝑦 βˆ’ 4 1 π‘₯ 𝑦 4 2 3 2 2 2
  • E βˆ’ 2 3 π‘₯ 𝑦 βˆ’ 4 9 π‘₯ 𝑦 βˆ’ 4 1 π‘₯ 𝑦 4 2 3 2 4 2

Q6:

Simplify 1 4 4 π‘₯ + 1 6 8 π‘₯ + 8 4 π‘₯ 1 2 π‘₯ + 3 π‘₯ + 1 9 π‘₯ + 1 8 2 0 1 7 1 2 1 2 8 5 .

  • A 1 5 π‘₯ + 3 3 π‘₯ + 2 5 3 2 2 9
  • B 9 π‘₯ + 5 π‘₯ + 1 1 8 5
  • C 9 π‘₯ + 5 π‘₯ + 1 1 3 2 2 9
  • D 1 5 π‘₯ + 3 3 π‘₯ + 2 5 8 5

Q7:

What is the height of a rectangular prism whose volume is and whose base is a square of side cm?

  • A cm
  • B cm
  • C cm
  • D cm
  • E cm

Q8:

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

  • A πœ‹
  • B 1 3 πœ‹
  • C 1 9
  • D 1 9 πœ‹
  • E 1 3

Q9:

What is the length of a rectangle whose area is ο€Ή 7 π‘₯ 𝑦 + 2 4 π‘₯ 𝑦 + 1 6 π‘₯ 𝑦  7 6 3 6 2 6 cm2 and whose width is π‘₯ 𝑦 cm?

  • A ο€Ή 7 π‘₯ 𝑦 + 2 4 π‘₯ 𝑦 βˆ’ 1 6 π‘₯ 𝑦  6 5 2 5 5 cm
  • B ο€Ή 7 π‘₯ 𝑦 βˆ’ 2 4 π‘₯ 𝑦 + 1 6 π‘₯ 𝑦  6 5 2 5 5 cm
  • C ο€Ή 7 π‘₯ 𝑦 + 2 4 π‘₯ 𝑦 + 1 6 π‘₯ 𝑦  6 6 2 6 6 cm
  • D ο€Ή 7 π‘₯ 𝑦 + 2 4 π‘₯ 𝑦 + 1 6 π‘₯ 𝑦  6 5 2 5 5 cm

Q10:

What is the length of a rectangle whose area is ο€Ή 2 1 π‘₯ 𝑦 + 2 3 π‘₯ 𝑦 + 2 0 π‘₯ 𝑦  6 6 4 6 3 6 cm2 and whose width is π‘₯ 𝑦 cm?

  • A ο€Ή 2 1 π‘₯ 𝑦 + 2 3 π‘₯ 𝑦 βˆ’ 2 0 π‘₯ 𝑦  5 5 3 5 2 5 cm
  • B ο€Ή 2 1 π‘₯ 𝑦 βˆ’ 2 3 π‘₯ 𝑦 + 2 0 π‘₯ 𝑦  5 5 3 5 2 5 cm
  • C ο€Ή 2 1 π‘₯ 𝑦 + 2 3 π‘₯ 𝑦 + 2 0 π‘₯ 𝑦  5 6 3 6 2 6 cm
  • D ο€Ή 2 1 π‘₯ 𝑦 + 2 3 π‘₯ 𝑦 + 2 0 π‘₯ 𝑦  5 5 3 5 2 5 cm

Q11:

The area of a triangle is ο€Ή 1 2 π‘₯ + 4 π‘₯  2 cm2, and its base is 4 π‘₯ m. Write an expression for its height.

  • A ο€Ή 4 8 π‘₯ + 1 6 π‘₯  3 2 cm
  • B ( 1 2 π‘₯ + 4 ) cm
  • C ( 3 π‘₯ + 1 ) cm
  • D ( 6 π‘₯ + 2 ) cm

Q12:

The area of a triangle is ο€Ή 7 π‘₯ + 3 π‘₯  2 cm2, and its base is 2 π‘₯ m. Write an expression for its height.

  • A ο€Ή 1 4 π‘₯ + 6 π‘₯  3 2 cm
  • B ( 1 4 π‘₯ + 6 ) cm
  • C ο€Ό 7 2 π‘₯ + 3 2  cm
  • D ( 7 π‘₯ + 3 ) cm

Q13:

The area of the shaded region in the figure below is ο€Ή 3 π‘₯ 𝑦 + 1 0 π‘₯ 𝑦    cm2. By considering the areas of the rectangles 𝐴 𝐡 𝐢 𝐷 and 𝑀 𝐸 𝑁 𝐹 , find the length of 𝐹 𝑁 .

  • A ( 9 π‘₯ 𝑦 + 8 6 ) cm
  • B ( 3 π‘₯ 𝑦 + 3 8 ) cm
  • C ( 9 π‘₯ 𝑦 + 3 8 ) cm
  • D ( 3 π‘₯ 𝑦 + 8 6 ) cm
  • E ( 3 π‘₯ 𝑦 + 5 8 ) cm

Q14:

The area of the shaded region in the figure below is ο€Ή 2 π‘₯ 𝑦 + 1 8 π‘₯ 𝑦    cm2. By considering the areas of the rectangles 𝐴 𝐡 𝐢 𝐷 and 𝑀 𝐸 𝑁 𝐹 , find the length of 𝐹 𝑁 .

  • A ( 8 π‘₯ 𝑦 + 1 2 6 ) cm
  • B ( 4 π‘₯ 𝑦 + 5 4 ) cm
  • C ( 8 π‘₯ 𝑦 + 5 4 ) cm
  • D ( 4 π‘₯ 𝑦 + 1 2 6 ) cm
  • E ( 4 π‘₯ 𝑦 + 9 0 ) cm

Q15:

Simplify 1 2 π‘Ž ο€Ή 1 1 π‘Ž 𝑏 βˆ’ 1 2 π‘Ž 𝑏  2 π‘Ž 𝑏 5 1 3 1 3 5 1 3 7 2 .

  • A 1 3 0 π‘Ž 𝑏 βˆ’ 1 4 2 π‘Ž 𝑏 1 1 1 1 3 1 1
  • B 6 6 π‘Ž 𝑏 βˆ’ 7 2 π‘Ž 𝑏 2 5 1 5 1 7 1 5
  • C 1 3 0 π‘Ž 𝑏 βˆ’ 1 4 2 π‘Ž 𝑏 2 5 1 5 1 7 1 5
  • D 6 6 π‘Ž 𝑏 βˆ’ 7 2 π‘Ž 𝑏 1 1 1 1 3 1 1