Lesson Worksheet: Polynomial Long Division without Remainder Mathematics • 10th Grade

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


Find the quotient of π‘₯+2π‘₯βˆ’3 divided by π‘₯βˆ’1.

  • Aπ‘₯+3π‘₯
  • Bπ‘₯+3
  • Cπ‘₯+3
  • Dπ‘₯βˆ’3π‘₯
  • Eπ‘₯βˆ’3


Find the quotient of 2π‘₯+3π‘₯+1 divided by π‘₯+1.

  • A2π‘₯+1
  • B2π‘₯βˆ’1
  • C2π‘₯+1
  • D2π‘₯+π‘₯
  • E2π‘₯βˆ’π‘₯


Find the quotient when 2π‘₯+7π‘₯βˆ’8π‘₯βˆ’21 is divided by 2π‘₯+3.

  • Aπ‘₯βˆ’2π‘₯βˆ’7
  • Bπ‘₯+2π‘₯+7
  • Cπ‘₯+7π‘₯βˆ’7
  • Dπ‘₯+7π‘₯+7
  • Eπ‘₯+2π‘₯βˆ’7


Find the quotient when βˆ’6π‘₯+11π‘₯+π‘₯βˆ’6 is divided by π‘₯βˆ’1.

  • Aβˆ’6π‘₯βˆ’5π‘₯βˆ’6
  • Bβˆ’6π‘₯βˆ’5π‘₯βˆ’6π‘₯
  • Cβˆ’6π‘₯+5π‘₯+6
  • Dβˆ’6π‘₯βˆ’5π‘₯+6
  • Eβˆ’6π‘₯+5π‘₯+6π‘₯


Find the quotient when 16π‘₯+12π‘₯βˆ’14π‘₯+6π‘₯οŠͺ is divided by 4π‘₯+6π‘₯.

  • A4π‘₯+3π‘₯+1
  • B4π‘₯+3π‘₯βˆ’1
  • C4π‘₯βˆ’3π‘₯+1
  • D4π‘₯βˆ’3π‘₯βˆ’1


Find the quotient when π‘₯βˆ’10π‘₯+16π‘₯βˆ’9π‘₯βˆ’4π‘₯+14οŠͺ is divided by π‘₯+2π‘₯βˆ’7.

  • Aπ‘₯βˆ’2π‘₯+π‘₯βˆ’2οŠͺ
  • Bπ‘₯+2π‘₯βˆ’π‘₯βˆ’2οŠͺ
  • Cπ‘₯+2π‘₯βˆ’π‘₯+2οŠͺ
  • Dπ‘₯βˆ’2π‘₯+π‘₯βˆ’2οŠͺ
  • Eπ‘₯βˆ’2π‘₯+π‘₯+2οŠͺ


Find the value of π‘Ž, where 2π‘₯+3π‘₯+π‘ŽοŠ¨ divided by π‘₯+1 has no remainder.


Find the value of π‘˜ that makes the expression 30π‘₯+57π‘₯βˆ’48π‘₯βˆ’20π‘₯+π‘˜οŠ«οŠ¨οŠ©οŠͺ divisible by 5π‘₯βˆ’8.


Given that the area of the rectangle in the diagram is 2π‘₯+π‘₯βˆ’5π‘₯βˆ’3, find an expression for the width of the rectangle.

  • Aπ‘₯βˆ’π‘₯+1
  • Bπ‘₯βˆ’1
  • Cπ‘₯βˆ’π‘₯βˆ’1
  • Dπ‘₯+π‘₯+1
  • Eπ‘₯βˆ’π‘₯


What is the width of a rectangle whose area is ο€Ήβˆ’π‘₯+20π‘₯+16π‘₯οŠͺ cm2 and whose length is ο€Ήβˆ’π‘₯+4π‘₯+4ο…οŠ¨ cm?

  • Aο€Ήβˆ’π‘₯+4π‘₯ο…οŠ¨ cm
  • Bο€Ήβˆ’π‘₯βˆ’4π‘₯ο…οŠ¨ cm
  • Cο€Ήπ‘₯βˆ’4π‘₯ο…οŠ¨ cm
  • Dο€Ήπ‘₯+4π‘₯ο…οŠ¨ cm

This lesson includes 19 additional questions and 207 additional question variations for subscribers.

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