Factoring Perfect Square Trinomial

2. 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

3. The first criteria of a Perfect
Square Trinomial is that it must
have three terms.
x2 + 8x + 16

4. The first term must be a perfect square
x2 = ( x )( x )
x2 + 8x + 16

5. The third term must be a perfect square
16 = ( 4 )( 4 )
x2 + 8x + 16

6. 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

7. 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?

8. 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.

9. x2 + 4x + 4
x
(x+2) 2 = (x+2) (x+2)
x2 + 4x + 4 = (x+2) (x+2) Factors
2+
Example:

10. = x + 5( )
2
x2 + 10x + 25
Another example:

11. 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

12. 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.

13. 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

14. 1. x2 – x + 1/4
2. 36m2 - 84m + 49
3. 4x2 - 12x + 9
4. p2 + 30p + 225
5. 64x2 - 176x + 121
Homework
Factor completely each of the following
expression.