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

Trinomials with leading coefficient of 1 x2 + bx + c

Trinomials with leading coefficient other than 1 ax2 + bx + c

Difference of Two Squares

Four term polynomial – factor by grouping

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 2. 15xy2 – 25x2y GCF: 4x

4x(4x2 – 3x + 1)GCF: 5xy5xy(3y – 5x)

Algebra II 4

3. 27m3p2 + 9mp - 54p2 4. 10x – 40y

GCF: 9p9p(3m3p + m – 6p)

GCF: 1010(x – 4y)

Algebra II 5

x2 + bx + c = (x + )(x + )

The product of these numbers is c.

The sum of these numbers is b.

Algebra II 6

Algebra II 7

(x – 14)(x + 2)

(x + 5)(x – 2)

(x + 7)(x + 5)

(y – 12)(x + 2)

prime

(p + 8)(p – 5)

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.

8Algebra II

How are we going to factor if the leading coefficient is not

1?

The “X” Method ax2 + bx + c

9Algebra II

a c

b

the “#s” are factors of a cthat add up to

b

#1 #2

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

10Algebra II

( )( )

Factor 8x2 – 14x + 5

Algebra II 11

4x– 5 2x – 1

40

-14

-4 -10

18

4215

( )( )

Factor 6x2 – 11x – 10

Algebra II 12

3x+2 2x – 5

-60

-11

-15 4

16

3211025

Factor 6x2 – 2x – 20 2(3x2 – x – 10)

2( )( )

Algebra II 13

3x+5 x – 2

-30

-1

-6 5

3111025

( )( )

Factor 21x2 – 13x + 2

Algebra II 14

3x– 1 7x – 2

42

-13

-6 -7

121

37

12

Factor 10a3 + 17a2 +3a a(10a2 + 17a + 3)

a( )

( )

Algebra II 15

2a+3 5a+1

30

17

2 15

110 13

25

( )( )

Factor 8x2 – x – 9

Algebra II 16

8x– 9 x + 1

-72

-1

8 -9

18

24

1933

Factor 4y2 – 2y – 12 2(2y2 – y – 6)

2( )( )

Algebra II 17

2y+3 y – 2

-12

-1

-4 3

21 1623

Factor 45a2 + 57a – 30 3(15a2 +19a – 10)

3( )( )

Algebra II 18

3a+5 5a – 2

-150

19

-6 25

115 1102535

( )( )

Factor 15x2 + 11x + 2

Algebra II 19

3x+1 5x+ 2

30

11

6 5

115

35

12

( )( )

Factor 15x2 – 29x – 2

Algebra II 20

15x + 1 x – 2

-30

-29

-30 1

115

35

12

(3x – 2)(x – 5)

(2x – 3)(2x + 1)

(7x – 1)(7x – 1)

prime

(5x + 7)(x + 2)

(3p – 5)(p + 2)

Algebra II 21

(x – 4)(8x + 3)

(3x + 1)(4x + 5)

prime

(2y + 1)(8y – 3)

(3x + 2)(3x + 2)

(2p – 1)(3p – 5)

Algebra II 22

Is it the difference of two Squares?

Factoring the Difference of Two Squares

a2 – b2 = (a + b)(a – b)

Algebra II 23

Factor: x2 – 9

(x – 3)(x + 3)

Algebra II 24

(2x – 3)(2x + 3)

(3x – 1)(3x + 1)

NOT A DIFF.

(1 – 5y)(1 + 5y)

(7y2 – 3z)(7y2 + 3z)

(9p – 5)(9p + 5)

Algebra II 25

prime

3(x2 – 9)3(x – 3)(x + 3)

4(x2 + x – 2)4(x – 1)(x + 2)

5(x2 – 4)5(x – 2)(x + 2)

2(7x2 + x – 6)2(7x – 6)(x + 1)

Algebra II 26

2u(u + 4)

2(5x2 + 17x + 14)2(5x + 7)(x + 2)

4x2(x2 – 16)4x2(x – 4)(x + 4)

3(10x2 – 19x + 7)3(2x – 1)(5x – 7)

Algebra II 27

If a polynomial has for terms: Factor the GCF out of the first two terms

Factor the GCF out of the second two terms

Factor out the common binomial and write as two binomials

28Algebra II

1.

29Algebra II