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Lesson: Factoring Perfect Trinomials

In this lesson, we will learn how to identify and factor quadratics that are perfect trinomials and how to complete the factorization.

Video

04:06

Sample Question Videos

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02:37
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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:

For which values of π‘˜ is π‘₯ + π‘˜ π‘₯ + 4 2 a perfect square?

  • A 4 , βˆ’ 4
  • B 3 , βˆ’ 3
  • C 6 , βˆ’ 6
  • D 2 , βˆ’ 2

Q3:

Complete the 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

Q4:

Complete the expression 8 1 π‘₯ + 2 5 2 to make a perfect square.

  • A + 9 0 π‘₯ βˆ’ 9 0 π‘₯ o r
  • B + 2 8 π‘₯ 2
  • C + 9 0 π‘₯ βˆ’ 9 0 π‘₯ 4 4 o r
  • D + 4 5 π‘₯ βˆ’ 4 5 π‘₯ o r
  • E + 9 0 π‘₯ 4

Q5:

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

Q6:

Complete the expression βˆ’ 4 8 π‘₯ + 9 2 to make a perfect square.

  • A 6 4 π‘₯ 4
  • B βˆ’ 1 6 π‘₯ 4
  • C 8 π‘₯
  • D βˆ’ 6 4 π‘₯ 4
  • E 1 6 π‘₯ 4

Q7:

By factoring or otherwise, evaluate .

  • A 64
  • B 80
  • C 48
  • D 106

Q8:

Completely factor .

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  • B
  • C
  • D
  • E

Q9:

Completely factor .

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  • D
  • E

Q10:

Completely factor .

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  • D
  • E

Q11:

Completely factor .

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  • D
  • E

Q12:

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

Q13:

If 9 π‘₯ + 3 0 π‘₯ + 𝑏 2 is a perfect square, what is the value of 𝑏 ?

Q14:

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

Q15:

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

Q16:

Completely factor .

  • A
  • B
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  • D
  • E

Q17:

Completely factor .

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  • E

Q18:

Completely factor .

  • A
  • B
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  • E

Q19:

Completely factor .

  • A
  • B
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  • E

Q20:

Completely factor .

  • A
  • B
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  • E

Q21:

Completely factor .

  • A
  • B
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  • D
  • E

Q22:

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

Q23:

If π‘˜ π‘₯ βˆ’ 2 4 π‘₯ + 3 6 2 is a perfect square, what is the value of π‘˜ ?

Q24:

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

Q25:

Which of the following is a perfect square?

  • A 2 5 𝑦 + 2 0 𝑦 + 4 2
  • B 2 5 𝑦 + 7 𝑦 + 4 2
  • C 2 5 𝑦 + 1 0 𝑦 + 4 2
  • D 𝑦 βˆ’ 2 5 2
  • E 𝑦 + 2 5 2
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