Name
Alg2A
Easter 2014 Assignment
Due: Monday, April 28, 2014
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)
6x2 – 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
Alg2A
Easter 2014 Assignment
Due: Monday, April 28, 2014
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
Alg2A
Easter 2014 Assignment
Due: Monday, April 28, 2014
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. (Keep the x2, or term with the highest exponent, POSITIVE)
(2) Factor completely.
(3) Set each factor to zero.
(3) Solve each
(4) State answer using solution set notation [fancy brackets { } ]
x2 – 48 = 13x
-13x -13x
2
x – 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
-30x +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
2
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
Alg2A
Easter 2014 Assignment
Due: Monday, April 28, 2014
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