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.

  • A3𝑥2
  • B2𝑥3
  • C3𝑥+2
  • D𝑥+3
  • E2𝑥+3

Q2:

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

  • A8𝑥2𝑥
  • B8𝑥+2𝑥
  • C8𝑥+2𝑥
  • D8𝑥2𝑥

Q3:

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

  • A6𝑥+5𝑥
  • B6𝑥5𝑥
  • C6𝑥+5𝑥
  • D6𝑥5𝑥

Q4:

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

  • A6𝑥6𝑥
  • B6𝑥+6𝑥
  • C6𝑥+6𝑥
  • D6𝑥6𝑥

Q5:

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

  • A3𝑥7𝑥
  • B3𝑥+7𝑥
  • C3𝑥+7𝑥
  • D3𝑥7𝑥

Q6:

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

  • A𝑥+1
  • B2𝑥+1
  • C2𝑥1
  • D𝑥1
  • E2𝑥2

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.

  • A3𝑥+2𝑥+1
  • B𝑥+3𝑥+2
  • C2𝑥+3𝑥1
  • D2𝑥+3𝑥+1
  • E3𝑥+2𝑥1

Q8:

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

  • A(2𝑦+2)
  • B(3𝑦1)
  • C(2𝑦2)
  • D(2𝑦+1)
  • E(2𝑦1)

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.

  • A𝑥1
  • B𝑥+2
  • C2𝑥2
  • D𝑥+1
  • E𝑥2

Q11:

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

  • A7𝑥
  • B35𝑥+7𝑥
  • C7𝑥+7𝑥
  • D7𝑥7𝑥

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?

  • A𝑥+4𝑥 cm
  • B𝑥4𝑥 cm
  • C𝑥4𝑥 cm
  • D𝑥+4𝑥 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.

  • A2𝑥+3
  • B2𝑥3
  • C3𝑥2
  • D𝑥+3
  • E3𝑥+2

Q16:

Use polynomial division to simplify 12𝑥21𝑥21𝑥+304𝑥3𝑥10.

  • A𝑥+1
  • B3(𝑥+1)
  • C3𝑥+7
  • D3(𝑥1)
  • E𝑥1

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?

  • A𝑦+3 cm
  • B𝑦+3 cm
  • C𝑦3 cm
  • D(𝑦+3) cm
  • E𝑦3 cm

Q18:

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

  • A3𝑥3𝑥 cm
  • B3𝑥+3𝑥 cm
  • C3𝑥3𝑥 cm
  • D3𝑥+3𝑥 cm

Q19:

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

  • A(6𝑥9) cm
  • B(𝑥8) cm
  • C(6𝑥18) cm
  • D(3𝑥9) 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.

  • A𝑥2
  • B3𝑥+2
  • C2𝑥3
  • D3𝑥2
  • E2𝑥+3

Q21:

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

  • A𝑥+3
  • B𝑥1
  • C𝑥+1
  • D𝑥3
  • E3𝑥3

Q22:

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

  • A8𝑥+2𝑥+2 cm
  • B8𝑥2𝑥+2 cm
  • C8𝑥2𝑥2 cm
  • D8𝑥+2𝑥2 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.

  • A9𝑥9𝑥
  • B9𝑥+9𝑥
  • C72𝑥+9𝑥
  • D9𝑥

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.

  • A2𝑥+1
  • B𝑥2
  • C𝑥+2
  • D𝑥1
  • E𝑥+1

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