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Lesson: Dividing Polynomials by a Divisor of Second Degree or Higher

Sample Question Videos

Worksheet • 6 Questions • 1 Video

Q1:

We want to factor โˆ’ 3 5 ๐‘ฅ + 7 ๐‘ฅ โˆ’ 4 2 ๐‘ฅ 3 2 4 into two factors. Given that one of these factors is ๐‘ฅ โˆ’ 6 ๐‘ฅ 2 , what is the other?

  • A 7 ๐‘ฅ + 7 ๐‘ฅ 2
  • B โˆ’ 3 5 ๐‘ฅ + 7 ๐‘ฅ 2
  • C 7 ๐‘ฅ โˆ’ 7 ๐‘ฅ 2
  • D 7 ๐‘ฅ 2

Q2:

Write 6 ๐‘ฅ โˆ’ 3 ๐‘ฅ โˆ’ 2 ๐‘ฅ + 3 ๐‘ฅ โˆ’ 5 2 ๐‘ฅ โˆ’ 3 ๐‘ฅ โˆ’ 3 ๐‘ฅ โˆ’ 4 ๏Šง ๏Šง ๏Šช ๏Šฉ ๏Šซ ๏Šจ in the form ๐‘ž ( ๐‘ฅ ) + ๐‘Ÿ ( ๐‘ฅ ) ๐‘‘ ( ๐‘ฅ ) .

  • A 3 ๐‘ฅ + 9 ๐‘ฅ 2 + 9 ๐‘ฅ 2 + 6 ๐‘ฅ + 2 7 4 + 2 4 ๐‘ฅ + + + + 2 2 2 ๐‘ฅ โˆ’ 3 ๐‘ฅ โˆ’ 3 ๐‘ฅ โˆ’ 4 ๏Šฌ ๏Šฉ ๏Šจ ๏Šช ๏Šฏ ๏Šซ ๏— ๏Šจ ๏Šจ ๏Šจ ๏Šซ ๏— ๏Šช ๏Šง ๏Šฎ ๏Šฏ ๏— ๏Šช ๏Šซ ๏Šจ ๏Žข ๏Žก
  • B 3 ๐‘ฅ + 9 ๐‘ฅ 2 + 9 ๐‘ฅ 2 + 2 ๐‘ฅ + 2 7 4 + + + 2 4 ๐‘ฅ + โˆ’ 2 2 2 ๐‘ฅ โˆ’ 3 ๐‘ฅ โˆ’ 3 ๐‘ฅ โˆ’ 4 ๏Šฌ ๏Šฉ ๏Šจ ๏Šง ๏Šญ ๏Šญ ๏— ๏Šช ๏Šญ ๏Šง ๏— ๏Šจ ๏Šจ ๏Šง ๏Šฆ ๏Šง ๏— ๏Šช ๏Šซ ๏Šจ ๏Žฃ ๏Žข
  • C 3 ๐‘ฅ + 9 ๐‘ฅ 2 + 9 ๐‘ฅ 2 + 6 ๐‘ฅ + 2 7 4 + 2 ๐‘ฅ โˆ’ 3 ๐‘ฅ โˆ’ 3 ๐‘ฅ โˆ’ 4 2 4 ๐‘ฅ + + + + 2 2 ๏Šฌ ๏Šฉ ๏Šจ ๏Šซ ๏Šจ ๏Šช ๏Šฏ ๏Šซ ๏— ๏Šจ ๏Šจ ๏Šจ ๏Šซ ๏— ๏Šช ๏Šง ๏Šฎ ๏Šฏ ๏— ๏Šช ๏Žข ๏Žก
  • D 3 ๐‘ฅ โˆ’ 9 ๐‘ฅ 2 โˆ’ 9 ๐‘ฅ 2 โˆ’ 2 ๐‘ฅ + 2 7 4 + 2 ๐‘ฅ โˆ’ 3 ๐‘ฅ โˆ’ 3 ๐‘ฅ โˆ’ 4 2 4 ๐‘ฅ + + โˆ’ โˆ’ 3 2 ๏Šฌ ๏Šฉ ๏Šจ ๏Šซ ๏Šจ ๏Šช ๏Šญ ๏Šง ๏— ๏Šจ ๏Šง ๏Šซ ๏— ๏Šช ๏Šฉ ๏Šญ ๏— ๏Šช ๏Žข ๏Žก
  • E 3 ๐‘ฅ โˆ’ 9 ๐‘ฅ 2 โˆ’ 9 ๐‘ฅ 2 โˆ’ 2 ๐‘ฅ + 2 7 4 + 2 4 ๐‘ฅ + + โˆ’ โˆ’ 3 2 2 ๐‘ฅ โˆ’ 3 ๐‘ฅ โˆ’ 3 ๐‘ฅ โˆ’ 4 ๏Šฌ ๏Šฉ ๏Šจ ๏Šช ๏Šญ ๏Šง ๏— ๏Šจ ๏Šง ๏Šซ ๏— ๏Šช ๏Šฉ ๏Šญ ๏— ๏Šช ๏Šซ ๏Šจ ๏Žข ๏Žก

Q3:

Knowing that the volume of a cylinder is ๐œ‹ ๏€น 4 ๐‘ฅ + 1 2 ๐‘ฅ โˆ’ 1 5 ๐‘ฅ โˆ’ 5 0 ๏… 3 2 and its radius is 2 ๐‘ฅ + 5 , express the height of the cylinder algebraically.

  • A ๐‘ฅ โˆ’ 2
  • B 2 ๐‘ฅ โˆ’ 2
  • C ๐‘ฅ + 2
  • D ๐‘ฅ + 1
  • E ๐‘ฅ โˆ’ 1

Q4:

What is the width of a rectangle whose area is ๏€น โˆ’ ๐‘ฅ + 2 0 ๐‘ฅ + 1 6 ๐‘ฅ ๏… 4 2 cm2 and whose length is ๏€น โˆ’ ๐‘ฅ + 4 ๐‘ฅ + 4 ๏… 2 cm?

  • A ๏€น ๐‘ฅ + 4 ๐‘ฅ ๏… 2 cm
  • B ๏€น ๐‘ฅ โˆ’ 4 ๐‘ฅ ๏… 2 cm
  • C ๏€น โˆ’ ๐‘ฅ + 4 ๐‘ฅ ๏… 2 cm
  • D ๏€น โˆ’ ๐‘ฅ โˆ’ 4 ๐‘ฅ ๏… 2 cm

Q5:

Find the quotient ๐‘ž ( ๐‘ฅ ) and the remainder ๐‘Ÿ ( ๐‘ฅ ) when 4 ๐‘ฅ โˆ’ 2 ๐‘ฅ โˆ’ 3 ๐‘ฅ + 4 ๐‘ฅ โˆ’ 5 7 6 4 is divided by 2 ๐‘ฅ โˆ’ 2 ๐‘ฅ โˆ’ 3 3 2 .

  • A ๐‘ž ( ๐‘ฅ ) = 2 ๐‘ฅ + ๐‘ฅ + ๐‘ฅ + 5 ๐‘ฅ 2 + 4 4 3 2 and ๐‘Ÿ ( ๐‘ฅ ) = 1 1 ๐‘ฅ + 2 3 ๐‘ฅ 2 + 7 2
  • B ๐‘ž ( ๐‘ฅ ) = 2 ๐‘ฅ + ๐‘ฅ + ๐‘ฅ + 5 ๐‘ฅ 2 + 4 4 3 2 and ๐‘Ÿ ( ๐‘ฅ ) = 2 2 ๐‘ฅ + 2 3 ๐‘ฅ + 1 4 2
  • C ๐‘ž ( ๐‘ฅ ) = 2 ๐‘ฅ โˆ’ 3 ๐‘ฅ + 6 ๐‘ฅ โˆ’ 2 1 ๐‘ฅ 2 + 1 5 4 3 2 and ๐‘Ÿ ( ๐‘ฅ ) = 4 8 ๐‘ฅ + 7 1 ๐‘ฅ 2 โˆ’ 4 0 2
  • D ๐‘ž ( ๐‘ฅ ) = 4 8 ๐‘ฅ + 7 1 ๐‘ฅ 2 โˆ’ 4 0 2 and ๐‘Ÿ ( ๐‘ฅ ) = 2 ๐‘ฅ โˆ’ 3 ๐‘ฅ + 6 ๐‘ฅ โˆ’ 2 1 ๐‘ฅ 2 + 1 5 4 3 2
  • E ๐‘ž ( ๐‘ฅ ) = 1 1 ๐‘ฅ + 2 3 ๐‘ฅ 2 + 7 2 and ๐‘Ÿ ( ๐‘ฅ ) = 2 ๐‘ฅ + ๐‘ฅ + ๐‘ฅ + 5 ๐‘ฅ 2 + 4 4 3 2

Q6:

Find the value of ๐‘˜ that makes the expression ๏€น 3 9 ๐‘ฅ โˆ’ 7 1 ๐‘ฅ โˆ’ 5 1 ๐‘ฅ + 2 8 ๐‘ฅ โˆ’ 5 4 ๐‘ฅ + ๐‘˜ ๏… 4 3 2 6 divisible by ๏€น 7 ๐‘ฅ โˆ’ 6 ๐‘ฅ โˆ’ 9 ๏… 3 .

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