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Worksheet: Factoring Quadratics

Q1:

Factorise fully 6 4 ( π‘₯ + 1 ) βˆ’ 9 ( π‘₯ βˆ’ 1 ) 2 2 .

  • A ( 1 1 π‘₯ + 1 1 ) ( 5 π‘₯ + 5 )
  • B ( 1 1 π‘₯ + 8 ) ( 5 π‘₯ + 3 )
  • C ( 8 π‘₯ + 1 1 ) ( 3 π‘₯ + 5 )
  • D ( 5 π‘₯ + 1 1 ) ( 1 1 π‘₯ + 5 )
  • E 2 4 ( π‘₯ + 1 ) ( π‘₯ βˆ’ 1 )

Q2:

Completely factor .

  • A
  • B
  • C
  • D
  • E

Q3:

Completely factor .

  • A
  • B
  • C
  • D
  • E

Q4:

Complete the following: π‘₯ βˆ’ 3 7 π‘₯ + 5 6 = ( 3 π‘₯ βˆ’ 8 ) ( ) 2 .

  • A2, 2 π‘₯ βˆ’ 7
  • B6, 2 π‘₯ + 7
  • C3, 2 π‘₯ βˆ’ 7
  • D6, 2 π‘₯ βˆ’ 7
  • E6, π‘₯ βˆ’ 7

Q5:

Expand and simplify ,then factor the result.

  • A
  • B
  • C
  • D

Q6:

Expand and simplify , then factor the result.

  • A
  • B
  • C
  • D

Q7:

Completely factor .

  • A
  • B
  • C
  • D

Q8:

Completely factor .

  • A
  • B
  • C
  • D
  • E

Q9:

Completely factor .

  • A
  • B
  • C
  • D

Q10:

Complete the following: 9 π‘₯ + 3 2 π‘₯ 𝑦 + = ( π‘₯ + 4 𝑦 ) ( ) 2 .

  • A 1 6 𝑦 2 , 9 π‘₯ βˆ’ 4
  • B βˆ’ 1 6 , 9 π‘₯ βˆ’ 4 𝑦
  • C 1 6 𝑦 2 , 4 π‘₯ + 9 𝑦
  • D βˆ’ 1 6 𝑦 2 , 9 π‘₯ βˆ’ 4 𝑦
  • E βˆ’ 1 6 , 4 π‘₯ + 9 𝑦

Q11:

Completely factor .

  • A
  • B
  • C
  • D
  • E

Q12:

Factor π‘₯ βˆ’ 8 π‘₯ + 1 2 2 .

  • A ( π‘₯ + 6 ) ( π‘₯ + 2 )
  • B ( π‘₯ βˆ’ 3 ) ( π‘₯ βˆ’ 4 )
  • C ( π‘₯ + 3 ) ( π‘₯ + 4 )
  • D ( π‘₯ βˆ’ 6 ) ( π‘₯ βˆ’ 2 )
  • E ( π‘₯ + 6 ) ( π‘₯ βˆ’ 2 )

Q13:

Complete the factoring: .

  • A
  • B
  • C
  • D
  • E

Q14:

Complete the following: 𝑧 + βˆ’ 1 6 = ( 𝑧 + ) ( + 2 ) 2 .

  • A βˆ’ 6 𝑧 , 8, 𝑧
  • B 6 𝑧 , βˆ’ 8 , 𝑧
  • C 6 𝑧 , 8, βˆ’ 8 𝑧
  • D βˆ’ 6 𝑧 , βˆ’ 8 , 𝑧
  • E βˆ’ 6 𝑧 , 14, βˆ’ 8 𝑧

Q15:

Expand and simplify , then factor the result completely.

  • A
  • B
  • C
  • D

Q16:

If π‘Ž βˆ’ 1 0 π‘Ž 𝑏 + 2 1 𝑏 = βˆ’ 3 0 2 2 and π‘Ž βˆ’ 3 𝑏 = βˆ’ 3 , what is the value of π‘Ž βˆ’ 7 𝑏 ?

Q17:

Factor 6 π‘₯ βˆ’ π‘₯ βˆ’ 1 2 2 .

  • A ( 2 π‘₯ + 3 ) ( 3 π‘₯ + 4 )
  • B ( 2 π‘₯ + 3 ) ( 3 π‘₯ βˆ’ 4 )
  • C ( 2 π‘₯ βˆ’ 3 ) ( 3 π‘₯ βˆ’ 4 )
  • D ( 2 π‘₯ βˆ’ 3 ) ( 3 π‘₯ + 4 )
  • E ( π‘₯ βˆ’ 4 ) ( π‘₯ + 3 )

Q18:

The expression can be factored. Given that is a negative integer, find the set of values of .

  • A
  • B
  • C
  • D
  • E

Q19:

The area of a rectangle is ο€Ή 5 π‘₯ + 1 2 π‘₯ + 7  2 cm2. Find its dimensions in terms of π‘₯ and its perimeter when π‘₯ = 4 .

  • A ( 5 π‘₯ βˆ’ 1 ) cm, ( π‘₯ + 7 ) cm, 60 cm
  • B ( 5 π‘₯ βˆ’ 7 ) cm, ( π‘₯ + 1 ) cm, 36 cm
  • C ( 5 π‘₯ βˆ’ 1 ) cm, ( π‘₯ βˆ’ 7 ) cm, 32 cm
  • D ( 5 π‘₯ + 7 ) cm, ( π‘₯ + 1 ) cm, 64 cm

Q20:

Completely factor .

  • A
  • B
  • C
  • D
  • E

Q21:

Completely factor .

  • A
  • B
  • C
  • D
  • E

Q22:

Complete the following: 8 π‘₯ = ( 4 π‘₯ + 7 𝑦 ) ( + 5 𝑦 ) 2 .

  • A + 3 4 π‘₯ 𝑦 + 3 5 2 ,
  • B + 3 5 π‘₯ 𝑦 + 3 4 𝑦 2 2 ,
  • C βˆ’ 3 4 π‘₯ 𝑦 + 3 5 𝑦 2 π‘₯ , 2
  • D + 3 4 π‘₯ 𝑦 + 3 5 𝑦 2 π‘₯ 2 ,
  • E + 3 4 π‘₯ 𝑦 + 3 5 𝑦 2 2 ,

Q23:

Completely factor .

  • A
  • B
  • C
  • D

Q24:

Expand and simplify , then factor the result completely.

  • A
  • B
  • C
  • D

Q25:

Completely factor .

  • A
  • B
  • C
  • D