Factoring Perfect Square Trinomial
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Transcript of 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.