Factoring Perfect Square Trinomial

1. (x + 4)2

2. (x + 5)2

= x2 + 8x + 16

= x2 + 10x + 25

3. (x + 7)2 = x2 + 14x + 49

4. (x - 9)2 = x2 - 18x + 81

5. (x - 11)2= x2 - 22x + 121

Drill

The first criteria of a Perfect

Square Trinomial is that it must

have three terms.

x2 + 8x + 16

The first term must be a perfect square

x2 = ( x )( x )

x2 + 8x + 16

The third term must be a perfect square

16 = ( 4 )( 4 )

x2 + 8x + 16

The middle term must be twice the

product of the square root coefficient

of the first and last term.

(2)(1)(4) = 8

x2 + 8x + 16

Perfect Square Trinomial

1. r2 – 8r + 16 YES

2. x2 – 14x + 49

3. d2 + 50d + 225

4. x2 + 2x + 1

5. b2 – 5b + 36

YES

YES

NO

NO

Yes or No?

WHAT IF IT IS A PERFECT SQUARE TRINOMIAL?

If you have a perfect Square Trinomial it is easy to factor:•Take the square root of the first term.•Take the square root of the last term.•Use the sign of the middle term, put in parenthesis and square the result.

x2 + 4x + 4

x

(x+2) 2 = (x+2) (x+2)

x2 + 4x + 4 = (x+2) (x+2) Factors

2+

Example:

= x + 5( )2

x2 + 10x + 25

Another example:

1. r2 – 8r + 16

Give the factors of the given examples.

= ( r – 4 )2

2. x2 – 14x + 49 = ( x – 7 )2

4. x2 + 2x + 1 = ( x + 1)2

Board Exercises

1. y2 - 6y + 9

2. a2 + 12a + 36

3. m2 - 18m + 81

4. y2 - 16y + 64

5. b2 - 12b + 36

Factor the following square trinomials.

Factor completely each of the following

expression.

1. x2 + 10x + 25

2. a2 - 8a + 16

3. 9x2 + 6xy + y2

4. x2 + 2x + 1

5. 169 + 26b + b2

Seatwork

1. x2 – x + 1/4

2. 36m2 - 84m + 49

3. 4x2 - 12x + 9

4. p2 + 30p + 225

5. 64x2 - 176x + 121

HomeworkFactor completely each of the following

expression.