Warm-up

Multiply.

1)

2)

3)

4)

€

(x + 3)(x − 3)

€

(m + 7)(m − 7)

€

(y +10)(y −10)

€

(t + 8)(t − 8)

€

=x2 − 9

€

=m2 − 49

€

=y2 −100

€

=t2 − 64

Factor.1)

2)

3)

4)

€

x2 − 9

€

m2 − 49

€

y2 −100

€

t 2 − 64

€

=(x + 3)(x − 3)

€

=(m + 7)(m − 7)

€

=(y +10)(y −10)

€

=(t + 8)(t − 8)

5)

6)

7)

€

x2 − y2

€

16 − k2

€

p2 −1

€

=(x + y)(x − y)

€

=(4 + k)(4 − k)

€

=(p +1)(p −1)

Objective - To recognize and use the Difference of Squares pattern.

Difference of Squares?

€

a2 − 25Factor.

€

=(a + 5)(a − 5)

PerfectSquare

PerfectSquare

minus

List the perfect squares from 1 to 200.149

16

25364964

81100121144

169196

Factor.

1)

2)

3)

4)

5)

6)

7)

8)

€

x2 − 81

€

9m2 −121

€

16 − 49k2

€

k4 − 4

€

t 2 − 50

€

4x2 − 49

€

36y2 −1

€

16x2 + 25

€

(x + 9)(x − 9)

€

(3m +11)(3m −11)

€

(4 + 7k)(4 − 7k)

€

(k2 + 2)(k2 − 2)

€

Not Factorable

€

(2x + 7)(2x − 7)

€

(6y +1)(6y −1)

€

Not Factorable

Objective - To recognize and factor a perfect square trinomial.

Find the area of the square in terms of x.

€

2x + 3

€

2x + 3

€

A = s2

Perfect Square Trinomial

€

A = (2x + 3)2

€

A = (2x + 3)(2x + 3)

€

A = 4x2 +12x + 9

Simplify by multiplying1)

2)

3)

4)

5)

6)

€

(x + 5)2

€

(m − 2)2

€

(2x + 7)2

€

(2k − 5)2

€

(3t + 4)2

€

(11− y)2

€

(x + 5)(x + 5)

€

x2 +10x + 25

€

(m − 2)(m − 2)

€

m2 − 4m + 4

€

(2x + 7)(2x + 7)

€

4x2 + 28x + 49

€

(2k − 5)(2k − 5)

€

4k2 − 20k + 25

€

(3t + 4)(3t + 4)

€

9t2 + 24t +16

€

(11− y)(11− y)

€

121− 22y + y2

Factor using the perfect square trinomial

1.) 16−9y2 2.) 4q2 −49

3.) 36−25x2 4.) x2 −18x+81

5.) 4n2 + 20n+ 25 6.) 16y2 +8y+1

Describe which pattern you would use to factor each of the

following.

1.) x2 −25

2.) x2 +8x+16

GCF - Greatest Common Factor Find the GCF of the following.

20 24

2 10

2 5

€

2 • 2 • 5

2 12

2 6

2 3

€

2 • 2 • 2 • 3

€

GCF =

€

2 • 2 = 4

Objective: Students will factor using a common factor

GCF - Greatest Common Factor

Find the GCF of the following.

9mn

6

€

2 • 3• m • m

9 mn

€

3• 3• m • n

€

GCF =

€

3• m = 3m

€

6m2

€

m2

m m2 3 m n3 3

GCF - Greatest Common Factor

Find the GCF of the following mentally.

1)

2)

3)

€

15x2y 12xy3

€

30a2b 42a3b2

€

14m4n3 21m5n2

€

3

€

x

€

y

€

6

€

a2

€

b

€

7

€

m4

€

n2

Find the missing factor.

1)

2)

3)

€

x10 = (x4 )( )

4)

5)

6)

€

8a4 = (2a)( )

€

2x2y = (x)( )

€

36a3b4 = (9ab)( )

€

7x4 y3 = (−xy2)( )

€

−6h2k3 = (3hk)( )

€

x6

€

4a3

€

2xy

€

4a2b3

€

−7x3y

€

−2hk2

Greatest Monomial Factor

Factor the greatest monomial factor.

1)

2)

3)

4)

€

12m4 −10m3

€

14a2 − 7a

€

15x3 − 20x2 + 30x

€

8x4y2 −12x3y3 − 20x4 y5

€

2m3 ( )

€

7a( )

€

5x( )

€

4x3y2 ( )

€

6m

€

−5

€

2a

€

−1

€

3x2

€

−4x

€

+ 6

€

2x

€

−3y

€

− 5xy3

Greatest Monomial Factor

Factor completely.

1)

2)

3)

4)

€

12a3 −16a2b

€

x4 y2 − x2y5

€

18a3b + 27a2b2 − 36a2b3

€

x5 + x4 + x2

€

4a2( )

€

x2y2( )

€

9a2b( )

€

x2( )

€

3a

€

− 4b

€

x2

€

− y3

€

2a

€

+ 3b

€

− 4b2

€

x3

€

+ x2

€

+ 1

Objective: To factor completely by finding a common factor.

1)

2)

€

2x2 − 50

€

2(x2 − 25)

€

2(x + 5)(x − 5)

Greatest Monomial Factor

Difference of Squares

€

m4 −1

€

(m2 +1)(m2 −1)

€

(m2 +1)(m +1)(m −1) Difference of Squares

Difference of Squares

Factor completely.3)

5)

€

3y2 − 27

€

x4 − 81

4)

6)

€

5m6 − 20

€

5y4 − 80

€

3(y2 − 9)

€

3(y + 3)(y − 3)

€

(x2 + 9)(x2 − 9)

€

(x2 + 9)(x + 3)(x − 3)

€

5(m6 − 4)

€

5(m3 + 2)(m3 − 2)

€

5(y4 −16)

€

5(y2 + 4)(y2 − 4)

€

5(y2 + 4)(y + 2)(y − 2)

Factor completely.7)

8)

€

3x2 − 24x + 48

€

3(x2 − 8x +16)

€

3(x − 4)2

€

x4 − 2x2 +1

€

(x2 −1)2

€

(x2 −1)(x2 −1)

€

(x +1)(x −1)

€

(x +1)2 (x −1)2

€

(x +1)(x −1)

Factor completely.9)

10)

€

5x2 + 30x + 45

€

5(x2 + 6x + 9)

€

5(x + 3)2

Greatest Monomial Factor

Perfect Square Trinomial

€

x4 − 8x2 +16

€

(x2 − 4)2

€

(x2 − 4)(x2 − 4)

Difference of Squares

Perfect Square Trinomial

€

(x + 2)(x − 2)

€

(x + 2)2 (x − 2)2

€

(x + 2)(x − 2)

1.) 2x2 +16x+14 2.) 3x3 −27x

3.) x3 + x2 −30x 4.) 2x3 +12x2 −14x

Factor completely.