1. 8-7 Factoring Special Cases
Please work on the following problems on your notes
(start before the bell rings):
Warm up:
#1: Multiply: (x – 5)(x + 5)
#2: y4 + 2x4y
a) Name polynomial (by terms)
b) Name polynomial (by degree)
c) Factor
#3: Factor
x3 + 2x2 + 9x + 18

2. 8-7 Factoring Special Cases
ANSWERS
#1: Multiply: (x – 5)(x + 5)
x2 + 5x – 5x – 25
x2 – 25
#2: y4 + 2x4y
a) Name polynomial (by terms)
Binomial
b) Name polynomial (by degree)
Quintic
c) Factor
-y(9y3 – 2x4)
#3: Factor
x3 + 2x2 + 9x + 18 x 2 x2 x3
2x2 9x 18 9
GCF: -y
(x2 + 9)(x + 2) OR
y(-9y3 + 2x4)

3. (Review) Multiply 1) (x + 3) (x – 3) x2 – 3x + 3x – 9 Ok…Do QUICKLY!!
What do you notice???
Ok…Do QUICKLY!!
4) (x + 7) (x – 7)
x2 – 49
How about..
5) (2x – 8)(2x + 8)
4x2 – 16x + 16x – 64
4x2 – 64

4. Difference of Squares OLD: Multiply (a + b)(a – b) = a2 – b2
NEW: Factor difference of squares
a2 – b2 = (a + b)(a – b)
Can take square root of both numbers/letters
Minus sign in the middle

5. Square Roots to Know

6. TOO: Is it a Difference of Squares?
x2 – 4
9x2 – 1
2x2 – 4
2x2 – 8
x2 + y2
x3 – 25
9xy – y2
-16 + x2
-4 – 16x2
x4 – 81
YES
NO √2
YES 2(x2 – 4)
NO Adding
NO x3
NO x
YES x2 – 16
NO (1 + 4x2)
YES √x4 = x2

7. Ex: FACTOR (difference of squares)
(x + 2)(x – 2)
(3x + 1)(3x – 1)
2(x2 – 4)
2(x + 2)(x – 2)
4) x2 – 16
(x + 4)(x – 4)
5) (x2 + 9)(x2 – 9)
(x2 + 9)(x + 3)(x – 3)
HINT: 2(x2 – 4)
HINT: x2 – 16

8. TOO - Review everything! x 1
6) Factor 3x2 – 3
3(x2 – 1)
3(x + 1)(x – 1)
7) Factor x3y + x
x(x2y + 1)
8) Factor 6x3 + 6x2 + 8x + 8
9) Factor 4x3 + 12x2 – 9x – 27
6x2
6x3
6x2
GCF 3 8 8x 8
GCF x
(6x2 + 8)(x + 1)
GCF 2
2(3x2 + 4)(x + 1)
(4x2 – 9 )(x + 3)
Diff of sq
(2x +3)(2x – 3)(x + 3)

9. Delta Math Homework Due Mon

10. Factor using 1) GCF 2) Grouping/Box 3) X – BOX 4) Difference of Squares 5) Perfect Square Trinomial
Question
#’s
Answer
16x2 – 40x – 24
81x4 – 16y4
y2 – 6y – 16
24x2 – 8
2x3 – 3x2 + 5x
n2 + 2n + 3mn + 6m
t3 – t2 + t – 1
4a3 + 8a2 + 4a
5x2 – 45y2
1 – 8u + 16u2
1&3
4&4 3 1 2
1&5
1&4 5
8(2x + 1)(x – 3)
(9x2 + 4y2)(3x + 2y)(3x – 2y)
(y – 8)(y + 2)
8(3x2 – 1)
x(2x2 – 3x + 5)
(n + 3m)(n + 2)
(t – 1)(t2 + 1)
4a(a + 1)2
5(x + 3y)(x – 3y)
(1 – 4u)2