Name Easter 2014 Assignment
Alg2A Due: Monday, April 28, 2014

Factoring Review

Case I w/ GCF (2Step) Case II: Case II w/ GCF:
7x2 + 77x – 84 6x2 – 5x – 4 20x2 + 14x + 2
7(x2 + 11x – 12) 2(10x2 + 7x + 1)
7(x + 12)(x – 1) 6x2 – 8x + 3x – 4 2(10x2 + 5x + 2x + 1)
2x | + 1 5x | + 1

(3x – 4) (3x - 4) (2x+1) (2x+1)
(3x - 4)(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

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 No GCF GCF then DOTS GCF then DOTS GCF then DOTS
x2 – 49 25x2 - 49 5x2 – 245 81x2 – 9 81x2 – 144
5(x2 – 49) 9(9x2 – 1) 9(9x2 – 16)

(x+7)(x-7) (5x+7)(5x-7) 5(x+7)(x-7) 9(3x+1)(3x-1) 9(3x+4)(3x-4)

(9x+3)(9x-3) is (9x+12)(9x-12) is

incorrect because incorrect because

there are “common there are “common

factors in your factors in your
factors.” 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

Solving Equations

Linear:
More than 1 x on the SAME side More than x on different sides
combine like terms move the x’s to one side
9x + 11 – 5x + 10 = -15 15x – 11 = 7x + 37

4x + 21 = -15 -7x - 7x

-21 -21 8x – 11 = 37

4x = -36 +11 +11

4 4 8x = 48

x = -9 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 bracketsà { } ]

x2 – 48 = 13x 2x3 = 30x2 – 112x 6x2 – 11x – 9 = 8x2 + 13x – 9
-13x -13x -30x2 +112x -30x2 + 112x -6x2 + 11x + 9 -6x2 + 11x + 9
x2 – 13x – 48 = 0 2x3 – 30x2 + 112x = 0 0 = 2x2 + 24x
(x+3) (x-16) = 0 2x(x2 – 15x + 56) = 0 0 = 2x(x + 12)

x+ 3= 0 x – 16 = 0 2x (x - 8) (x - 7) = 0 2x = 0 x + 12 = 0
-3 -3 +16 +16 2x=0 x-8 = 0 x-7=0 2 2 -12 -12
x = -3 x = 16 2 2 +8 +8 +7 +7 x = 0 x = -12
x=0 x = 8 x = 7


x = {-3,16} x = {0,7,8} x = {-12,0}

Examples:


6) 3(8x + 6) = 8(4x + 2) 7) 5(11x – 5) – 7(9x - 2) = 37

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