1. 
The height of an object launched t seconds is modeled
by h(t) = -16t2 + 32t + 25. Find the vertex and
interpret what it means. What is the height of the
object after 1.5 seconds? 2. 
The table below shows the average sale price p of a
house in Suffolk County, Massachusetts for various
years since 1988. Use your graphing calculator to find
a quadratic model for this data. If this trend continues,
what would the cost of a house be in 2010? Algebra II
1
Factoring Quadratics
Algebra II
¡  Greatest
Common Factor
¡  Difference
of Two Squares
¡  Trinomials with leading
of 1 à x2 + bx + c
coefficient
¡  Trinomials
with leading coefficient
other than 1 à ax2 + bx + c
Algebra II
3
Take out the greatest common factor
of a trinomial by dividing each term by
the GCF (greatest common factor)
Examples:
1. 16x3 – 12x2 + 4x
GCF: 4x
4x(4x2 – 3x + 1)
Algebra II
2. 15xy2 – 25x2y GCF: 5xy
5xy(3y – 5x)
4
3. 27m3p2 + 9mp - 54p2 4. 10x – 40y
CF: 9p
G
9p(3m3p + m – 6p)
GCF: 10
10(x – 4y)
Algebra II
5
Factoring the Difference of
Two Squares
a2 – b2 = (a + b)(a – b)
Algebra II
6
Factor: x2 – 9
Algebra II
(x – 3)(x + 3)
7
1. 
4x2 – 9
4. 
(2x – 3)(2x + 3)
2. 
9x2 – 1
(1 – 5y)(1 + 5y)
5. 
(3x – 1)(3x + 1)
3. 
16x2 + 25
prime
NOT
A DIFF.
Algebra II
1 – 25y2
49y4 – 9z2
(7y2 – 3z)(7y2 + 3z)
6. 
81p2 – 25
(9p – 5)(9p + 5)
8
The product of these numbers is c.
x2 + bx + c = (x + )(x + )
The sum of these numbers is b.
Algebra II
9
x2 – 12x – 28 4.  y2 – 10y – 24
(x – 14)(x + 2)
(y – 12)(x + 2)
2.  x2 + 3x – 10 5.  x2 – 6x + 10
(x + 5)(x – 2)
prime
3.  x2 + 12x + 35 6.  p2 + 3p – 40
1. 
(x + 7)(x + 5)
Algebra II
(p + 8)(p – 5)
10
¡  You
should always check your factoring
results by multiplying the factored
polynomial to verify that it is equal to
the original polynomial.
¡  You
can detect computational errors or
errors in the signs of your numbers by
checking your results.
Algebra II
11
How are we going to factor if the
leading coefficient is not 1?
¡  The
“X” Method
x2 + bx + c
a
the “#s” are
factors of a Ÿ c
that add up to b
Algebra II
a Ÿ c
#1
#2
b
12
¡  It
is actually a graphic
organization of “guess & check”
¡  The
“#s” are not what go in the
binomials
¡  Completely
unnecessary if the
leading coefficient is 1
Algebra II
13
Factor 8x2 – 14x + 5
( 4x – 5 ) ( 2x – 1 )
Algebra II
40
-4
-10
-14
14
Factor 6x2 – 11x – 10
( 3x + 2 ) ( 2x – 5 )
Algebra II
-60
-15
4
-11
15
Factor 6x2 – 2x – 20
2(3x2 – x – 10)
2( 3x + 5 ) ( x – 2 )
Algebra II
-30
-6
5
-1
16
Factor 21x2 – 13x + 2
( 3x – 1 ) ( 7x – 2 )
Algebra II
42
-6
-7
-13
17
Factor 10a3 + 17a2 +3a
a(10a2 + 17a + 3)
a(2a + 3 )( 5a + 1 )
Algebra II
30
2
15
17
18
Factor 8x2 – x – 9
( 8x – 9 ) ( x + 1 )
Algebra II
-72
8
-9
-1
19
Factor 4y2 – 2y – 12
2(2y2 – y – 6)
2( 2y + 3 ) ( y – 2 )
Algebra II
-12
-4
3
-1
20
Factor 45a2 + 57a – 30
3(15a2 +19a – 10)
3( 3a + 5 ) ( 5a – 2 )
Algebra II
-150
-6
25
19
21
Factor 15x2 + 11x + 2
( 3x + 1 ) ( 5x + 2 )
Algebra II
30
6
5
11
22
Factor 15x2 – 29x – 2
( 15x + 1) ( x – 2 )
Algebra II
-30
-30
1
-29
23
11.  3x2
– 17x + 10
14.  16y2
(3x – 2)(x – 5)
12.  4x2
– 4x – 3
(2x – 3)(2x + 1)
13.  49x2
– 14x + 1
(7x – 1)(7x – 1)
Algebra II
+ 4y + 1
prime
15.  5x2
+ 17x + 14
(5x + 7)(x + 2)
16.  3p2
+ p - 10
(3p – 5)(p + 2)
24
17.  8x2
– 29x – 12
(x – 4)(8x + 3)
18.  12x2
+ 19x + 5
(3x + 1)(4x + 5)
19.  4x2
– 10x + 3
prime
Algebra II
20.  16y2
+ 2y – 3
(2y + 1)(8y – 3)
21.  9x2
+ 12x + 4
(3x + 2)(3x + 2)
22.  6p2
– 13p + 5
(2p – 1)(3p – 5)
25
1. 
3x2 – 27
3(x2 – 9)
3(x – 3)(x + 3)
3. 
2. 
4x2 + 4x – 8
4. 
4(x2 + x – 2)
4(x – 1)(x + 2)
Algebra II
5x2 – 20
5(x2 – 4)
5(x – 2)(x + 2)
14x2 + 2x - 12
2(7x2 + x – 6)
2(7x – 6)(x + 1)
26
5. 
2u2 + 8u
2u(u + 4)
7. 
6. 
10x2 + 34x + 28
8. 
2(5x2 + 17x + 14)
2(5x + 7)(x + 2)
Algebra II
4x4 – 64x2
4x2(x2 – 16)
4x2(x – 4)(x + 4)
30x2 – 57x + 21
3(10x2 – 19x + 7)
3(2x – 1)(5x – 7)
27