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Lesson: Factoring Perfect Trinomials

Video

04:06

Sample Question Videos

Worksheet • 25 Questions • 4 Videos

Q1:

For which values of π‘˜ is 1 6 π‘₯ + π‘˜ π‘₯ + 8 1 2 a perfect square?

  • A 7 2 , βˆ’ 7 2
  • B 1 3 , βˆ’ 1 3
  • C 2 6 , βˆ’ 2 6
  • D 3 6 , βˆ’ 3 6

Q2:

Complete the expression 1 6 π‘₯ + 𝑦 4 2 to make a perfect square.

  • A + 8 π‘₯ 𝑦 βˆ’ 8 π‘₯ 𝑦 2 2 o r
  • B + 4 π‘₯ 𝑦 βˆ’ 4 π‘₯ 𝑦 2 2 o r
  • C + 8 π‘₯ 𝑦 βˆ’ 8 π‘₯ 𝑦 o r
  • D + 1 0 π‘₯ 𝑦 βˆ’ 1 0 π‘₯ 𝑦 2 2 o r

Q3:

Which of the following is a perfect square?

  • A π‘₯ βˆ’ 1 8 π‘₯ + 8 1 2
  • B π‘₯ βˆ’ 1 8 π‘₯ βˆ’ 8 1 2
  • C π‘₯ βˆ’ 9 π‘₯ + 8 1 2
  • D π‘₯ βˆ’ 8 1 2
  • E π‘₯ + 8 1 2

Q4:

Complete the quadratic expression 9 π‘₯ + 1 4 4 2 to make a perfect square.

  • A + 7 2 π‘₯ βˆ’ 7 2 π‘₯ o r
  • B + 3 0 π‘₯ 2
  • C + 7 2 π‘₯ βˆ’ 7 2 π‘₯ 4 4 o r
  • D + 3 6 π‘₯ βˆ’ 3 6 π‘₯ o r
  • E + 7 2 π‘₯ 4

Q5:

If 9 𝑦 + 3 0 𝑦 + 𝑏 2 is a perfect square, what is the value of 𝑏 ?

Q6:

Complete the expression βˆ’ 6 0 π‘₯ + 2 5 2 to make a perfect square.

  • A 3 6 π‘₯ 4
  • B βˆ’ 1 2 π‘₯ 4
  • C 6 π‘₯
  • D βˆ’ 3 6 π‘₯ 4
  • E 1 2 π‘₯ 4

Q7:

Complete the expression 4 2 5 π‘Ž + 1 9 𝑏 2 2 to make a perfect square.

  • A Β± 4 1 5 π‘Ž 𝑏
  • B + 2 5 π‘Ž 𝑏
  • C Β± 2 1 5 π‘Ž 𝑏
  • D Β± 4 1 5 π‘Ž 𝑏 2
  • E + 4 5 π‘Ž 𝑏

Q8:

If π‘˜ 𝑦 βˆ’ 2 4 𝑦 + 9 2 is a perfect square, what is the value of π‘˜ ?

Q9:

Factorise fully 9 π‘₯ + 3 6 π‘₯ 𝑦 + 3 6 𝑦 4 2 2 4 .

  • A 9 ( π‘₯ + 2 𝑦 ) 2 2 2
  • B 9 ( 𝑦 + 2 π‘₯ ) 2
  • C 9 ( 2 π‘₯ + 𝑦 ) 2 2 2
  • D 9 ( π‘₯ + 2 𝑦 ) 2
  • E ( π‘₯ + 2 𝑦 ) 2 2 2

Q10:

Factorise fully π‘₯ βˆ’ 1 0 π‘₯ 𝑦 + 2 5 𝑦 2 2 .

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

Q11:

By factorising or otherwise, evaluate ( 1 0 . 1 ) βˆ’ 4 . 2 Γ— 1 0 . 1 + ( 2 . 1 ) 2 2 .

Q12:

Factorise fully 8 1 π‘š + 1 8 π‘š + 1 2 .

  • A ( 9 π‘š + 1 ) 2
  • B ( π‘š βˆ’ 9 ) 2
  • C ( π‘š + 9 ) 2
  • D ( 9 π‘š + 1 ) ( 9 π‘š βˆ’ 1 )
  • E ( 9 π‘š + 1 ) ( π‘š + 9 )

Q13:

Factorise fully 4 ( π‘₯ βˆ’ 7 ) βˆ’ 1 6 ( π‘₯ βˆ’ 7 ) ( 𝑦 βˆ’ 6 ) + 1 6 ( 𝑦 βˆ’ 6 ) 2 2 .

  • A ( 2 π‘₯ βˆ’ 4 𝑦 + 1 0 ) 2
  • B ο€Ή 2 π‘₯ βˆ’ 4 𝑦 + 1 0  2 2 2
  • C ( 2 π‘₯ βˆ’ 4 𝑦 ) 2
  • D ( π‘₯ + 𝑦 βˆ’ 2 ) 2
  • E ( 2 π‘₯ βˆ’ 4 𝑦 βˆ’ 3 8 ) 2

Q14:

Complete the expression 8 1 π‘₯ + 9 0 π‘₯ 𝑦 + β‹― 2 to make a perfect square.

  • A 2 5 𝑦 2
  • B 9 𝑦
  • C 2 0 𝑦 2
  • D βˆ’ 2 5 𝑦
  • E 2 5 𝑦

Q15:

Factorise fully 4 9 8 1 π‘₯ + 8 9 π‘₯ + 1 6 4 9 2 .

  • A ο€Ό 7 9 π‘₯ + 4 7  2
  • B ο€Ό 7 9 π‘₯ βˆ’ 2 7  2
  • C ο€Ό 7 9 π‘₯ βˆ’ 4 7  2
  • D ο€Ό 7 9 π‘₯ + 2 7  2
  • E ο€Ό 7 9 π‘₯ + 4 7  2 2

Q16:

Expand and simplify 5 π‘₯ ( 5 π‘₯ + 1 8 𝑦 ) + 8 1 𝑦  , then factorise the result.

  • A ( 5 π‘₯ + 9 𝑦 ) 
  • B ( 5 π‘₯ + 8 ) 
  • C ( 5 π‘₯ βˆ’ 9 𝑦 ) 
  • D ( 5 π‘₯ + 8 𝑦 ) 
  • E ( 5 π‘₯ + 9 ) 

Q17:

By factorising or otherwise, evaluate ( 9 7 ) + 6 Γ— 9 7 + 9  .

Q18:

Factorise fully 0 . 1 6 𝑏 + 7 . 2 𝑏 + 8 1 2 .

  • A ( 0 . 4 𝑏 + 9 ) 2
  • B ( 0 . 2 + 9 𝑏 ) 2
  • C ( 0 . 2 𝑏 + 9 ) 2
  • D ( 0 . 4 + 9 𝑏 ) 2
  • E ( 0 . 4 ( 𝑏 + 9 ) ) 2

Q19:

Factorise fully 1 3 6 π‘₯ βˆ’ π‘₯ + 9 2 .

  • A ο€Ό 1 6 π‘₯ βˆ’ 3  2
  • B ( 6 π‘₯ βˆ’ 3 ) 2
  • C ο€Ό 1 6 π‘₯ + 3  ο€Ό 1 6 π‘₯ βˆ’ 3 
  • D ο€Ό 3 π‘₯ βˆ’ 1 6  2
  • E ο€Ό 3 π‘₯ + 1 6  ο€Ό 3 π‘₯ βˆ’ 1 6 

Q20:

Given that π‘₯ + 2 π‘₯ 𝑦 + 𝑦 = 8 1 2 2 , what are the possible values of π‘₯ + 𝑦 ?

  • A 9 , βˆ’ 9
  • B 1 8 , βˆ’ 1 8
  • C 4 0 , βˆ’ 4 0
  • D 8 1 , βˆ’ 8 1

Q21:

Factorise fully π‘Ž + 6 π‘Ž + 9 π‘Ž οŠͺ  .

  • A π‘Ž ( 3 π‘Ž + 1 )  
  • B π‘Ž ( 3 π‘Ž + 1 )  
  • C π‘Ž ( π‘Ž + 3 )  
  • D π‘Ž ( 3 π‘Ž + 1 ) ( 3 π‘Ž βˆ’ 1 )  
  • E ( π‘Ž + 3 )  

Q22:

Factorise fully 6 4 𝑦 π‘₯ βˆ’ 6 4 𝑦 π‘₯ + 1 6 𝑦 2 .

  • A 1 6 𝑦 ( 2 π‘₯ βˆ’ 1 ) 2
  • B 1 6 π‘₯ ( 8 βˆ’ 4 𝑦 ) 2
  • C 1 6 𝑦 ( 8 βˆ’ 4 π‘₯ ) 2
  • D 1 6 ( 8 π‘₯ + 4 ) ( 8 π‘₯ βˆ’ 4 )
  • E 1 6 𝑦 ( 2 π‘₯ + 1 ) 2

Q23:

Write all possible expressions for π‘˜ such that π‘₯ + π‘˜ + 4 𝑦 2 2 is a perfect square.

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

Q24:

Factorise fully ( π‘Ž + 4 𝑏 ) + 1 4 𝑐 ( π‘Ž + 4 𝑏 ) + 4 9 𝑐 2 2 4 .

  • A ο€Ή π‘Ž + 4 𝑏 + 7 𝑐  2 2
  • B ο€Ή π‘Ž + 4 𝑏 βˆ’ 7 𝑐  2 2
  • C ( π‘Ž + 4 𝑏 + 7 𝑐 ) 2
  • D ο€Ή π‘Ž + 4 𝑏 + 4 9 𝑐  2 2
  • E ο€Ή π‘Ž + 4 𝑏 + 1 4 𝑐  2 2

Q25:

Expand and simplify ( 3 π‘₯ + 𝑦 ) βˆ’ 1 2 π‘₯ 𝑦 2 , and then factorise the result completely.

  • A ( 3 π‘₯ βˆ’ 𝑦 ) 2
  • B ( 3 π‘₯ + 𝑦 ) 2
  • C ( 3 π‘₯ + 1 ) 2
  • D ( 3 π‘₯ βˆ’ 1 ) 2
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