Worksheet: Dividing Polynomials by Binomials Using Factorization

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In this worksheet, we will practice dividing polynomials by binomials using factorization.

Q1:

Find the value of 𝑘 that makes the expression 𝑥−𝑘𝑥+30 divisible by 𝑥−5.

Q2:

The area of a triangle is 12𝑥+38𝑥+28 cm2 and its base is (2𝑥+4) cm. Write an expression for its height.

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

Q3:

What is the width of a rectangle whose area is 4𝑥−32𝑥+6𝑥 cm2 and whose length is 8𝑥+3𝑥 cm?

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

Q4:

By factoring, find all the solutions to 𝑥−𝑥−14𝑥+24=0, given that (𝑥+4) is a factor of 𝑥−𝑥−14𝑥+24.

  • 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+2𝑦+5𝑦+10 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 126 cm.
  • BThe length is (𝑦+5) cm, and the perimeter is 15 cm.
  • CThe length is 𝑦−5 cm, and the perimeter is 34 cm.
  • DThe length is 𝑦+5 cm, and the perimeter is 54 cm.
  • EThe length is (𝑦+5) cm, and the perimeter is 30 cm.

Q6:

Knowing that the length of a rectangle is 2𝑥+5 and its area is 4𝑥+10𝑥+6𝑥+15, express the width of the rectangle algebraically.

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

Q7:

Knowing that the volume of a box is 10𝑥+30𝑥−8𝑥−24, its length is 2, and its width is 𝑥+3, express the height of the box algebraically.

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

Q8:

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

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

Q9:

Find the value of 𝑘 that makes the expression 𝑥−𝑘𝑥+20 divisible by 𝑥−5.

Q10:

Find the value of 𝑘 that makes the expression 𝑥−𝑘𝑥−18 divisible by 𝑥+2.

Q11:

The area of a triangle is 18𝑥+73𝑥+35 cm2 and its base is (2𝑥+7) cm. Write an expression for its height.

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

Q12:

The area of a triangle is 48𝑥+62𝑥+9 cm2 and its base is (8𝑥+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 37𝑥+35𝑥+6𝑥 cm2 and whose length is 7𝑥+6𝑥 cm?

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

Q14:

What is the width of a rectangle whose area is 30𝑥+15𝑥+15𝑥 cm2 and whose length is 5𝑥+5𝑥 cm?

  • A 3 𝑥 − 3 𝑥 cm
  • B 3 𝑥 cm
  • C 3 0 𝑥 + 3 𝑥 cm
  • D 3 𝑥 + 3 𝑥 cm

Q15:

A rectangle has an area of 𝑦+10𝑦+7𝑦+70 cm2 and a width of (𝑦+10) cm. Find its length in terms of 𝑦 and its perimeter when 𝑦=2.

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

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