Name
Alg1
Easter 2013 Assignment
Due: Monday, April 8, 2013
Factoring Review
Case I w/ GCF (2Step) Case II:
Case II w/ GCF:
7x2 + 77x – 84
7(x2 + 11x – 12)
7(x + 12)(x – 1)
x2 – 8x + 3x – 4
2x | + 1
(3x – 4) (3x - 4)
(3x - 4)(2x + 1)
20x2 + 14x + 2
2(10x2 + 7x + 1)
2(10x2 + 5x + 2x + 1)
5x
| +1
(2x+1) (2x+1)
2(5x + 1)(2x + 1)
Examples:
1) a) 16x2 – 16x – 96
b) 16x2 - 2x – 3
c) 16x2 + 28x + 10
2) (order will be mixed up)
a) 12x2 – 38x + 6
b) 12x2 – 4x – 5
c) 12x2 + 48x – 540
3) (order will be mixed up)
a) 20x2 + 29x + 5
b) 20x2 – 100x – 1,680
c) 20x2 – 28x + 8
6x2 – 5x – 4
Name
Alg1
Easter 2013 Assignment
Due: Monday, April 8, 2013
DOTS (Difference Of Two Squares):
You MUST check for a GCF 1st on all factoring problems… even if it looks like it will be
straight DOTS. You cannot have “common factors in your factors”!!
No GCF
x2 – 49
(x+7)(x-7)
No GCF
25x2 - 49
GCF then DOTS
5x2 – 245
5(x2 – 49)
(5x+7)(5x-7) 5(x+7)(x-7)
GCF then DOTS
81x2 – 9
9(9x2 – 1)
9(3x+1)(3x-1)
GCF then DOTS
81x2 – 144
9(9x2 – 16)
9(3x+4)(3x-4)
(9x+3)(9x-3) is
incorrect because
there are “common
factors in your
factors.”
(9x+12)(9x-12) is
incorrect because
there are “common
factors in your
factors.”
4) a) x2 – 100
b) 121x2 – 100
c) 25x2 – 100
d) 225x2 – 100
e) 3x2 – 48
f) 196x2 – 16
5) a) 9x2 – 25
b) x2 – 256
c) 6x2 – 726
d) 144x2 – 36
e) 144x2 – 169
f) 144x2 – 196
Name
Alg1
Easter 2013 Assignment
Due: Monday, April 8, 2013
Solving Equations
Linear:
More than 1 x on the SAME side
combine like terms
More than x on different sides
move the x’s to one side
9x + 11 – 5x + 10 = -15
4x + 21 = -15
-21 -21
4x
= -36
4
4
x
= -9
15x – 11 = 7x + 37
-7x
- 7x
8x – 11 = 37
+11
+11
8x
= 48
8
8
x
=6
Quadratic (there is an “x2” in the equation):
(1) Set the equation equal to zero.
(2) Set each factor to zero.
(3) Solve each
(4) State answer using solution set notation [fancy brackets { } ]
x2 – 48 = 13x
-13x -13x
x2 – 13x – 48 = 0
(x+3) (x-16) = 0
x+ 3= 0 x – 16 = 0
-3 -3
+16 +16
x = -3
x = 16
x = {-3,16}
2x3 = 30x2 – 112x
-30x2 +112x -30x2 + 112x
2x3 – 30x2 + 112x = 0
2x(x2 – 15x + 56) = 0
2x (x - 8) (x - 7) = 0
2x=0 x-8 = 0 x-7=0
2 2 +8 +8 +7 +7
x=0 x = 8 x = 7
x = {0,7,8}
6x2 – 11x – 9 = 8x2 + 13x – 9
-6x2 + 11x + 9 -6x2 + 11x + 9
0 = 2x2 + 24x
0 = 2x(x + 12)
2x = 0 x + 12 = 0
2
2
-12
-12
x=0
x = -12
x = {-12,0}
Examples:
6) 3(8x + 6) = 8(4x + 2)
7) 5(11x – 5) – 7(9x - 2) = 37
Name
Alg1
Easter 2013 Assignment
Due: Monday, April 8, 2013
8) 3x3 = -39x2 – 120x
9) x2 – 45 = 2x2 – 17x + 21
10) x2 = 2x + 48
11) 9(6x + 3) + 8(2x - 11) = -271
12) 6(6x + 1) = 19(3x - 3)
13) 7x2 – 8x – 12 = 4x2 + 10x - 12