Perfect Square Trinomials

Factoring Perfect Square Trinomials

A trinomial (as the prefix "tri-" suggests) is a polynomial with three terms. When we're dealing with perfect squares, it means we're dealing with squaring binomials.

Multiple Choice

Find the Square root of 4

$$\sqrt{4}$$  

• 16

• 8

• 4

• 2

Multiple Choice

$$What\ is\ the\ \sqrt{m^2}$$  ?

• m

• 2m

• $$m^2$$  

• $$m^4$$  

Multiple Choice

$$Find\ the\ value\ of\ \sqrt{100.}\$$  

• 100

• 50

• 10

• 5

Multiple Choice

Evaluate

$$Evaluate\ \sqrt{16.}$$  

• 32

• 16

• 8

• 4

Multiple Choice

What is the

$$What\ is\ the\ \sqrt{64\ ?}$$  

• 8

• 16

• 32

• 12

Multiple Choice

Simplify: 4²

• 4

• 8

• 16

• 64

Multiple Choice

Evaluate 5².

• 5

• 10

• 25

• 55

Multiple Choice

Simplify (2x)²

• 2x²

• 4x

• 4x²

• 2x

The following are the tips on how to recognize a perfect square trinomial:

• Check whether the first and last terms of the trinomial are perfect squares

• Multiply the roots of the first and third terms together.

• Compare to the middle terms with the result in step two

• If the first and last terms are perfect squares, and the coefficient of the middle term is twice the product of the square roots of the first and last terms, then, the expression is a prefect square trinomial.

   

Multiple Select

Check all the expressions that are trinomials.

• x² + 2x + 1

• 2x - 2r + 3y

• x² - 4

• x³

• x³ - 4x² + 4

Multiple Select

Which of the following term is a perfect square? Check all your answers.

• x²

• 4y²

• 12

• 10

• 25

How to determine if the polynomial is a perfect square trinomial?

To recognize if a trinomial is perfect square is to look at its first and third term. If they are both squares, there's a good chance that you may be working with a perfect square trinomial.

Multiple Select

Which of the following expressions an example of a perfect square trinomials?

• n² + 5x + 6

• x² + 8x + 16

• 4m² - 12m + 9

• a² - 25

How to Factor a Perfect Square Trinomial?

• Identify the squared numbers in the first and third terms of the trinomial

• Examine the middle term if it has either positive or negative. If the middle term of the trinomial is positive or negative, then the factors will have a plus and minus sign respectively.

• Write out your terms by applying the following identities:

•  a² + 2ab + b² = (a + b)² = (a + b) (a + b)

•  a² – 2ab + b² = (a – b)² = (a – b) (a – b)

Factor x² + 8x + 16

• Write the expression x² + 8x + 16 as a² + 2ab + b²

• x² + 8x + 16 ⟹ (x)² + 2 (x) (4) + (4)²

• = (x + 4)²

• = (x + 4) (x + 4)

• 
  

Factor x²+ 6x + 9

Solution

We can rewrite the expression x² + 6x + 9 in the form a² + 2ab + b² as;

x²+ 6x + 9 ⟹ (x)² + 2 (x) (3) + (3)²

Applying the formula of a² + 2ab + b² = (a + b)² to the expression gives;

= (x + 3)²

= (x + 3) (x + 3)

Factor 4a² – 4ab + b²

• 4a² – 4ab + b² ⟹ (2a)² – (2)(2) ab + b²

  
  

  
  

• = (2a – b)²

• = (2a – b) (2a – b)

• 
  

Multiple Choice

Which of the following are the factors of x² + 10x + 25?

• (x+5) (x+5)

• (x+5) (x-5)

• (x-5) (x-5)

• (x+10) (x+15)

Multiple Choice

What are the factors of m² - 6m + 9?

• (m-3) (m-6)

• (m+3) (m+3)

• (m+3) (m-3)

• (m-3) (m-3)

Multiple Choice

Find the factors of 4x² + 20x + 25

• (4x+5) (4x+5)

• (4x-5) (4x-5)

• (2x+5) (2x+5)

• (2x-5) (2x-5)

Multiple Select

Is x² - 2x - 1 factorable?

• Yes

• No

Multiple Select

Is x² + 4x - 4 a perfect square trinomial?

• Yes

• No

Multiple Select

Is x² - 20x + 100 a perfect square trinomial?

• Yes

• No

Multiple Select

Is 2x²+ 8x + 8 factorable?

• Yes

• No

Open Ended

Give the factors of n² + 12n + 36.

Multiple Choice

Find the factors of 4x² + 20x + 25

• (4x+5) (4x+5)

• (4x-5) (4x-5)

• (2x+5) (2x+5)

• (2x-5) (2x-5)