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 1 2 ๐‘ฅ + 2 0 ๐‘ฅ โˆ’ 2 1 ๐‘ฅ โˆ’ 3 6 3 2 , its length is 2 ๐‘ฅ + 3 , and its width is 3 ๐‘ฅ โˆ’ 4 , express the height of the box algebraically.

  • A 3 ๐‘ฅ + 2
  • B 2 ๐‘ฅ โˆ’ 3
  • C 3 ๐‘ฅ โˆ’ 2
  • D 2 ๐‘ฅ + 3
  • E ๐‘ฅ + 3

Q2:

Find the quotient of โˆ’ 6 4 ๐‘ฅ + 1 2 ๐‘ฅ โˆ’ 2 ๐‘ฅ ๏Šช ๏Šจ divided by โˆ’ 8 ๐‘ฅ โˆ’ 2 ๐‘ฅ + 1 ๏Šจ .

  • A โˆ’ 8 ๐‘ฅ + 2 ๐‘ฅ ๏Šจ
  • B 8 ๐‘ฅ + 2 ๐‘ฅ ๏Šจ
  • C โˆ’ 8 ๐‘ฅ โˆ’ 2 ๐‘ฅ ๏Šจ
  • D 8 ๐‘ฅ โˆ’ 2 ๐‘ฅ ๏Šจ

Q3:

Find the quotient when 6 ๐‘ฅ + 1 1 ๐‘ฅ โˆ’ 4 3 ๐‘ฅ โˆ’ 4 0 ๐‘ฅ ๏Šช ๏Šฉ ๏Šจ is divided by ๐‘ฅ + ๐‘ฅ โˆ’ 8 ๏Šจ .

  • A โˆ’ 6 ๐‘ฅ โˆ’ 5 ๐‘ฅ ๏Šจ
  • B 6 ๐‘ฅ โˆ’ 5 ๐‘ฅ ๏Šจ
  • C โˆ’ 6 ๐‘ฅ + 5 ๐‘ฅ ๏Šจ
  • D 6 ๐‘ฅ + 5 ๐‘ฅ ๏Šจ

Q4:

We want to factor 1 8 ๐‘ฅ โˆ’ 4 8 ๐‘ฅ + 3 0 ๐‘ฅ ๏Šช ๏Šจ into two factors. Given that one of these factors is 3 ๐‘ฅ + 3 ๐‘ฅ โˆ’ 5 ๏Šจ , what is the other?

  • A โˆ’ 6 ๐‘ฅ + 6 ๐‘ฅ ๏Šจ
  • B 6 ๐‘ฅ + 6 ๐‘ฅ ๏Šจ
  • C โˆ’ 6 ๐‘ฅ โˆ’ 6 ๐‘ฅ ๏Šจ
  • D 6 ๐‘ฅ โˆ’ 6 ๐‘ฅ ๏Šจ

Q5:

We want to factor 6 ๐‘ฅ โˆ’ 2 0 ๐‘ฅ โˆ’ 7 ๐‘ฅ + 4 9 ๐‘ฅ ๏Šช ๏Šฉ ๏Šจ into two factors. Given that one of these factors is 2 ๐‘ฅ โˆ’ 2 ๐‘ฅ โˆ’ 7 ๏Šจ , what is the other?

  • A โˆ’ 3 ๐‘ฅ + 7 ๐‘ฅ ๏Šจ
  • B 3 ๐‘ฅ + 7 ๐‘ฅ ๏Šจ
  • C โˆ’ 3 ๐‘ฅ โˆ’ 7 ๐‘ฅ ๏Šจ
  • D 3 ๐‘ฅ โˆ’ 7 ๐‘ฅ ๏Šจ

Q6:

Evaluate ๐‘š รท ( ๐‘› ๐‘ ) , given that ๐‘š = 3 5 , ๐‘ = โˆ’ 5 , and ๐‘› = โˆ’ 7 .

Q7:

Karim spent 540 seconds jogging. Make a table to determine the algebraic expression that relates the number of s e c o n d s ๐‘› to that of minutes, given that there are 60 seconds in 1 minute. Then, determine how many m i n u t e s Karim spent jogging.

  • A ๐‘› รท 6 , 90 min
  • B 6 0 + ๐‘› , 600 min
  • C 6 0 ๐‘› , 8 min
  • D ๐‘› รท 6 0 , 9 min
  • E ๐‘› โˆ’ 6 0 , 480 min

Q8:

โˆ’ 4 0 ๐‘ฅ รท = โˆ’ 5 ๐‘ฅ 9 7 .

  • A 1 8 ๐‘ฅ 2
  • B 8 ๐‘ฅ 1 6
  • C 2 0 0 ๐‘ฅ 1 6
  • D 8 ๐‘ฅ 2

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