Upload
virgil-baldwin
View
220
Download
0
Embed Size (px)
Citation preview
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.