Worksheet: Dividing a Polynomial by a Binomial Using Factorization

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In this worksheet, we will practice dividing polynomials by polynomials using factorization and finding common factors that will cancel out.

Q1:

Find the value of 𝑘 that makes the expression 𝑥 − 𝑘 𝑥 + 3 0 2 divisible by 𝑥 − 5 .

Q2:

The area of a triangle is 1 2 𝑥 + 3 8 𝑥 + 2 8 2 cm2 and its base is ( 2 𝑥 + 4 ) cm. Write an expression for its height.

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

Q3:

What is the width of a rectangle whose area is 4 𝑥 − 3 2 𝑥 + 6 𝑥 3 2 4 cm2 and whose length is 8 𝑥 + 3 𝑥 2 cm?

  • A 2 𝑥 2 cm
  • B 4 𝑥 − 4 𝑥 2 cm
  • C 2 𝑥 + 4 𝑥 2 cm
  • D 2 𝑥 − 4 𝑥 2 cm

Q4:

By factoring, find all the solutions to 𝑥 − 𝑥 − 1 4 𝑥 + 2 4 = 0 3 2 , given that ( 𝑥 + 4 ) is a factor of 𝑥 − 𝑥 − 1 4 𝑥 + 2 4 3 2 .

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

Q5:

A rectangle has an area of 𝑦 + 2 𝑦 + 5 𝑦 + 1 0 3 2 cm2 and a width of ( 𝑦 + 2 ) cm. Find its length in terms of 𝑦 and its perimeter when 𝑦 = 4 .

  • AThe length is ( 𝑦 + 5 ) cm, and the perimeter is 30 cm.
  • BThe length is 𝑦 − 5 2 cm, and the perimeter is 34 cm.
  • CThe length is ( 𝑦 + 5 ) cm, and the perimeter is 15 cm.
  • DThe length is 𝑦 + 5 2 cm, and the perimeter is 54 cm.
  • EThe length is 𝑦 + 5 2 cm, and the perimeter is 126 cm.

Q6:

Knowing that the length of a rectangle is 2 𝑥 + 5 and its area is 4 𝑥 + 1 0 𝑥 + 6 𝑥 + 1 5 3 2 , express the width of the rectangle algebraically.

  • A 3 𝑥 + 2 2
  • B 2 𝑥 − 3 2
  • C 3 𝑥 − 2 2
  • D 2 𝑥 + 3 2
  • E 𝑥 + 3 2

Q7:

Knowing that the volume of a box is 1 0 𝑥 + 3 0 𝑥 − 8 𝑥 − 2 4 3 2 , its length is 2, and its width is 𝑥 + 3 , express the height of the box algebraically.

  • A 4 𝑥 − 5 2
  • B 5 𝑥 + 4 2
  • C 4 𝑥 + 5 2
  • D 5 𝑥 − 4 2
  • E 5 𝑥 − 2 2

Q8:

⋯ + 5 0 𝑎 𝑏 + 3 8 𝑎 𝑏 ⋯ = − 2 1 𝑎 𝑏 + 2 5 𝑏 + 1 9 2 .

  • A 4 0 𝑎 𝑏 2 2 , 2 𝑎 𝑏
  • B 4 2 𝑎 𝑏 2 2 , − 2 𝑎 𝑏
  • C − 4 0 𝑎 𝑏 2 2 , 2 𝑎 𝑏
  • D − 4 2 𝑎 𝑏 2 2 , 2 𝑎 𝑏

Q9:

Find the value of 𝑘 that makes the expression 𝑥 − 𝑘 𝑥 + 2 0 2 divisible by 𝑥 − 5 .

Q10:

Find the value of 𝑘 that makes the expression 𝑥 − 𝑘 𝑥 − 1 8 2 divisible by 𝑥 + 2 .

Q11:

The area of a triangle is 1 8 𝑥 + 7 3 𝑥 + 3 5 2 cm2 and its base is ( 2 𝑥 + 7 ) cm. Write an expression for its height.

  • A ( 9 𝑥 + 1 0 ) cm
  • B ( 9 𝑥 + 5 ) cm
  • C ( 1 8 𝑥 + 5 ) cm
  • D ( 1 8 𝑥 + 1 0 ) cm

Q12:

The area of a triangle is 4 8 𝑥 + 6 2 𝑥 + 9 2 cm2 and its base is ( 8 𝑥 + 9 ) cm. Write an expression for its height.

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

Q13:

What is the width of a rectangle whose area is 1 4 𝑥 + 7 2 𝑥 − 8 𝑥 4 2 6 cm2 and whose length is 8 𝑥 − 2 𝑥 3 cm?

  • A 4 𝑥 3 cm
  • B 1 4 𝑥 + 9 𝑥 3 cm
  • C 4 𝑥 − 9 𝑥 3 cm
  • D 4 𝑥 + 9 𝑥 3 cm

Q14:

What is the width of a rectangle whose area is 5 9 𝑥 − 3 6 𝑥 + 7 𝑥 5 4 6 cm2 and whose length is 9 𝑥 + 𝑥 2 3 cm?

  • A 7 𝑥 3 cm
  • B 5 9 𝑥 − 4 𝑥 3 2 cm
  • C 7 𝑥 + 4 𝑥 3 2 cm
  • D 7 𝑥 − 4 𝑥 3 2 cm

Q15:

A rectangle has an area of 𝑦 + 1 0 𝑦 + 7 𝑦 + 7 0 3 2 cm2 and a width of ( 𝑦 + 1 0 ) cm. Find its length in terms of 𝑦 and its perimeter when 𝑦 = 2 .

  • AThe length is ( 𝑦 + 7 ) cm, and the perimeter is 42 cm.
  • BThe length is 𝑦 + 7 2 cm, and the perimeter is 46 cm.
  • CThe length is ( 𝑦 + 7 ) cm, and the perimeter is 21 cm.
  • DThe length is 𝑦 + 7 2 cm, and the perimeter is 46 cm.
  • EThe length is 𝑦 + 7 2 cm, and the perimeter is 132 cm.

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