Lesson Worksheet: Polynomial Long Division without Remainder Mathematics

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

Q1:

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

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

Q2:

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

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

Q3:

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

Q4:

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

Q5:

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)

Q6:

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

Q7:

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

Q8:

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

Q9:

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

Q10:

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

Q11:

Use polynomial division to simplify 12𝑥21𝑥21𝑥+304𝑥3𝑥10.

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

Q12:

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

Q13:

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

Q14:

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

Q15:

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

Q16:

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

Q17:

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

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

Q18:

Find the quotient when 𝑥8𝑥+20𝑥21 is divided by 𝑥+2𝑥7.

  • A𝑥𝑥+3
  • B𝑥2𝑥+3
  • C𝑥+2𝑥3
  • D𝑥+2𝑥+3
  • E𝑥2𝑥3

Q19:

Find the quotient when 𝑥10𝑥+16𝑥9𝑥4𝑥+14 is divided by 𝑥+2𝑥7.

  • A𝑥2𝑥+𝑥2
  • B𝑥+2𝑥𝑥2
  • C𝑥+2𝑥𝑥+2
  • D𝑥2𝑥+𝑥2
  • E𝑥2𝑥+𝑥+2

Q20:

Use polynomial division to simplify 6𝑥+5𝑥20𝑥212𝑥+3.

  • A𝑥+52𝑥7
  • B3𝑥2𝑥7
  • C𝑥2𝑥7
  • D3𝑥+2𝑥7
  • E3𝑥+52𝑥7

Q21:

We want to factor 32𝑥+100𝑥+35𝑥63𝑥 into two factors. Given that one of these factors is 4𝑥+9𝑥, what is the other?

  • A8𝑥7𝑥7
  • B8𝑥+7𝑥7
  • C8𝑥7𝑥+7
  • D8𝑥+7𝑥+7

Q22:

Find the quotient when 16𝑥+12𝑥14𝑥+6𝑥 is divided by 4𝑥+6𝑥.

  • A4𝑥+3𝑥+1
  • B4𝑥+3𝑥1
  • C4𝑥3𝑥+1
  • D4𝑥3𝑥1

Q23:

Find the quotient when 2𝑥+7𝑥8𝑥21 is divided by 2𝑥+3.

  • A𝑥2𝑥7
  • B𝑥+2𝑥+7
  • C𝑥+7𝑥7
  • D𝑥+7𝑥+7
  • E𝑥+2𝑥7

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