Worksheet: Polynomial Long Division without Remainder

In this worksheet, we will practice performing long division on polynomials.

Q1:

Knowing that the volume of a box is 12𝑥+20𝑥21𝑥36, its length is 2𝑥+3, and its width is 3𝑥4, express the height of the box algebraically.

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

Q2:

Find the quotient of 64𝑥+12𝑥2𝑥 divided by 8𝑥2𝑥+1.

  • A 8 𝑥 2 𝑥
  • B 8 𝑥 + 2 𝑥
  • C 8 𝑥 + 2 𝑥
  • D 8 𝑥 2 𝑥

Q3:

Find the quotient when 6𝑥+11𝑥43𝑥40𝑥 is divided by 𝑥+𝑥8.

  • A 6 𝑥 + 5 𝑥
  • B 6 𝑥 5 𝑥
  • C 6 𝑥 + 5 𝑥
  • D 6 𝑥 5 𝑥

Q4:

We want to factor 18𝑥48𝑥+30𝑥 into two factors. Given that one of these factors is 3𝑥+3𝑥5, what is the other?

  • A 6 𝑥 6 𝑥
  • B 6 𝑥 + 6 𝑥
  • C 6 𝑥 + 6 𝑥
  • D 6 𝑥 6 𝑥

Q5:

We want to factor 6𝑥20𝑥7𝑥+49𝑥 into two factors. Given that one of these factors is 2𝑥2𝑥7, what is the other?

  • A 3 𝑥 7 𝑥
  • B 3 𝑥 + 7 𝑥
  • C 3 𝑥 + 7 𝑥
  • D 3 𝑥 7 𝑥

Q6:

Knowing that the length of a rectangle is 𝑥+5 and its area is 2𝑥+9𝑥5, express the width of the rectangle algebraically.

  • A 𝑥 + 1
  • B 2 𝑥 + 1
  • C 2 𝑥 1
  • D 𝑥 1
  • E 2 𝑥 2

Q7:

Knowing that the length of a rectangle is 3𝑥4 and its area is 6𝑥8𝑥+9𝑥9𝑥4, express the width of the rectangle as a polynomial in standard form.

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

Q8:

The expression 4𝑦+8𝑦5 has two factors. One factor is (2𝑦+5), what is the other factor?

  • A ( 2 𝑦 + 2 )
  • B ( 3 𝑦 1 )
  • C ( 2 𝑦 2 )
  • D ( 2 𝑦 + 1 )
  • E ( 2 𝑦 1 )

Q9:

Find the value of 𝑎 given that 6𝑥+𝑎𝑥30𝑥21𝑥+10 is divisible by (2𝑥+5).

Q10:

Knowing that the volume of a cylinder is 𝜋4𝑥+12𝑥15𝑥50 and its radius is 2𝑥+5, express the height of the cylinder algebraically.

  • A 𝑥 1
  • B 𝑥 + 2
  • C 2 𝑥 2
  • D 𝑥 + 1
  • E 𝑥 2

Q11:

We want to factor 35𝑥+7𝑥42𝑥 into two factors. Given that one of these factors is 𝑥6𝑥, what is the other?

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

Q12:

Find the value of 𝑘 that makes the expression 30𝑥+57𝑥48𝑥20𝑥+𝑘 divisible by 5𝑥8.

Q13:

What is the width of a rectangle whose area is 𝑥+20𝑥+16𝑥 cm2 and whose length is 𝑥+4𝑥+4 cm?

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

Q14:

Find the value of 𝑘 that makes the expression 39𝑥71𝑥51𝑥+28𝑥54𝑥+𝑘 divisible by 7𝑥6𝑥9.

Q15:

Knowing that the volume of a box is 18𝑥21𝑥40𝑥+48, its length is 3𝑥4, and its width is 3𝑥4, express the height of the box algebraically.

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

Q16:

Use polynomial division to simplify 12𝑥21𝑥21𝑥+304𝑥3𝑥10.

  • A 𝑥 + 1
  • B 3 ( 𝑥 + 1 )
  • C 3 𝑥 + 7
  • D 3 ( 𝑥 1 )
  • E 𝑥 1

Q17:

The area of triangle 𝐴𝐵𝐶 is 12𝑦+4𝑦+3𝑦+12 cm2. Its altitude, 𝐴𝐷, is 𝑦+4 cm. What is its base length, 𝐵𝐶?

  • A 𝑦 + 3 cm
  • B 𝑦 + 3 cm
  • C 𝑦 3 cm
  • D ( 𝑦 + 3 ) cm
  • E 𝑦 3 cm

Q18:

What is the width of a rectangle whose area is 9𝑥+27𝑥39𝑥+21𝑥 cm2 and whose length is 3𝑥+6𝑥7 cm?

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

Q19:

Determine the perimeter of the rectangle whose area is 2𝑥17𝑥+8 cm2, given that its length is (2𝑥1) cm.

  • A ( 6 𝑥 9 ) cm
  • B ( 𝑥 8 ) cm
  • C ( 6 𝑥 1 8 ) cm
  • D ( 3 𝑥 9 ) cm

Q20:

The volume of a cylinder is 𝜋3𝑥+24𝑥+46𝑥16𝑥32 and its radius is 𝑥+4. Write, in its simplest form, a polynomial for the height of the cylinder.

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

Q21:

The volume of a cylinder is 𝜋25𝑥65𝑥29𝑥3. Given that its radius is 5𝑥+1, find an expression for its height.

  • A 𝑥 + 3
  • B 𝑥 1
  • C 𝑥 + 1
  • D 𝑥 3
  • E 3 𝑥 3

Q22:

What is the width of a rectangle whose area is 24𝑥78𝑥12𝑥+18𝑥 cm2 and whose length is 3𝑥+9𝑥 cm?

  • A 8 𝑥 + 2 𝑥 + 2 cm
  • B 8 𝑥 2 𝑥 + 2 cm
  • C 8 𝑥 2 𝑥 2 cm
  • D 8 𝑥 + 2 𝑥 2 cm

Q23:

What must be added to 21𝑥+71𝑥+23 to give an expression that is divisible by 7𝑥+5?

Q24:

Find the quotient when 72𝑥+54𝑥+18𝑥 is divided by 6𝑥+2𝑥.

  • A 9 𝑥 9 𝑥
  • B 9 𝑥 + 9 𝑥
  • C 7 2 𝑥 + 9 𝑥
  • D 9 𝑥

Q25:

The volume of a box is 10𝑥+27𝑥+2𝑥24. Given that its length is 5𝑥4 and its width is 2𝑥+3, express the height of the box algebraically.

  • A 2 𝑥 + 1
  • B 𝑥 2
  • C 𝑥 + 2
  • D 𝑥 1
  • E 𝑥 + 1

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