Cut the Squares Apart

Algebra I: Factoring 1 Cut the squares apart. Match equivalent expressions. You should get a new 4 X 4 square. REVIEW (x-2)(x+2) (4x-1)2 (6x+1)(x-2) (x+1)(x-1) 2 ) ) ) ) 6 x 6 4 3 4 - - x x 2 + - - x x 2 2 x x 1 x - + ( ( 4 ) ) 2 2 4 5 1 - ( ( x 2 4 x 1 3 ) - + + + 6 x 2 1 x x 2 + + 2 ( ( 4 6 x 3 ( x2+6x+9 x2-10x+24 25x2-16 6x2+41x+30 (x+3)2 (x-4)(x-6) (5x-4) (x+6)(6x+5) (5x+4) x 2 ) ) ) 2 ) 9 + 9 6 8 x x 2 - x 6 + + 2 2 x + 2 + + x x x + ( x ( ( ) - 3 7 1 ) ) 3 1 2 x x ( 2 3 2 - 6 - - - - x x 1 1 x x ( + ( ( 8 8 4

4x2-25 x2-9 16x2-1 x2-7x+12 (2x+5)(2x- (x+3)(x-3) (4x-1) (x-4)(x-3) 5) (4x+1) x ) ) ) 2 ( - 5 8 5 ( 4 2 - - x 4 x + 6 x x x 2 x + x x - ( ( - ( 6 2 ) ) 2 5 1 ) + - x 2 3 ) 5 x 2 x ( - + + - x + 1 - 2 x x 5 - x 6 ( ( 1 ( ) )

x2+4x+3 7x2- 9x2-4 x2-8x+16 19x+10 (x+3)(x+1) (7x-5)(x- (3x-2)(3x+2) (x-4)2 2) 2 ) ) ) ) 4 1 1 4 3 5 x - + + x x 2 x + x x x 2 + ( 2 x - 2 ( + ) 2 + 2 x ) 2 ( 3 2 0 ( - 1 ) 1 1 x - + x 6 5 2 - - x x + 1 ( x 3 2 ( 2 ( 25x2+20x+ x2+9 x2+3x-10 x2-15 4

1 Algebra I: Factoring 2 Cut the squares apart. Match equivalent expressions. You should get a new 4 X 4 square.

x2+3x+2 (x-3)(x-4) 2x2+8x-10 x2-y2 2 6 3 ( ( - ( 1 x x + + 2 y y + + + y x x - 2 y 5 2 y 5 1 2 - + y ) ) ) + + + ( ( ( 2 2 2 4 - x y x 1 y y x x + - + - 2 + 2 y 1 6 ) ) )

(x-3)(x+4) (2x-1)(x- (2x+1)(x-1) (x-5)(x+1) 3) (1-y)(2-y) x2+5x+6 6x2+5x-4 (x+7)(x-1) 2 4 2 7 ( y ( - - 1 y 2 + 2 2 x + + x + x + x 5 y 2 y 6 3 - x 2 + x - 2 - 3 ) 2 ) 2 4 ( 5 x ( 1 x y x 1 x + 6 + 2 + + - - 2 x x 3 2 y 6 ) ) 3

y2-7y+10 (2x-1)(x- (3x-4)(2x-1) 2(x+1)(x-5) 1) 2x2-x-1 2x2-4x+6 - x2-2x-3 (x-3)(x-3) 2 4 2 6 ( ( ( - 5 x y + + x x x - ( + x x + 7 3 - 4 - y 5 2 4 2 ) 1 + - x ( 2 x ) ) + 3 2 - ( ( 2 x 2 x x - y x 2 6 x - + ) - x 5 4 3 3 ) ) )

(x+2)(x+3) 2(3+x)(1- 2(x+5)(x-1) y2-3y+2 x) 2x2+4x-6 (x-y)(x-y) (3-x)(1+x) (2x-1)(x+3)

5 9 0 1 (

( - - ( x 1 2 y 2 x ( x - + x + - x - 4 x 4 5 1 - x - 8 3 ) 2 ) ) 7 - ( ( ( ) x 2 1 y x x ( - x x + 2 - + 2 1 + 3 x 2 ) 3 ) 2 ) ) 2(1+x)(3-x) x2+9 x2+y2 x2-7x+12

2 Algebra 2 Name______Exit- Factoring sum and difference of 2 cubes Date ______

16x2 - 4

27x3 - 8

125 + x3

Algebra 2 Name______Exit- Factoring by Grouping Date ______

Factor each by grouping:

1) 2x 2  3x 1 2) 3x 2  8x  35

3) x3  4x 2  3x 12

3 Algebra 2 Name______HW- Mixed Factoring Practice Date ______

Factor completely: 1) 18a 2  9a 2) x 2  5x  6 3) 2x 2  2x  4

______4) 7x 2  34x  5 5) 14b 2  5b  6 6) 54z 3 16

______7) 8x 3  64 8) 64x 2 z 8  4y 2 9) 16x 4  2xy 3

______10) 32x 6  8y12 11) 3ax 12bx  2a  8b 12) x 4  x3 y  x  y

4 Algebra 2 Name______Exit- Undefined Rational Expressions Date ______

Determine the values for which each fraction is undefined. Then simplify completely.

Algebra 2 Name______Exit- Simplify Rational Expressions Date ______

Simplify each, if possible.

x 2  5x  6 12 p 2  6 p  6 1. 2. x 2  2x 15 4( p 1) 2

5 Algebra 2 Name______HW- Simplify Rational Expressions Date ______

Objective: To Determine When a Fraction is Undefined and to Simplify Rational Expressions

HW: For HRW Homework Help Online, go to 8-2 Exercises. See Examples 1 & 2. http://my.hrw.com/math06_07/nsmedia/homework_help/alg2/alg2_ch08_02_homeworkhelp.html

Also, in the Online Textbook, see Example 2 under Tech Keys to find out how to check your answers.

Determine the value(s) that make the following rational expressions undefined. Then simplify completely. 2x  7 x 2  4x  4 1) 2) x  7 x 2  4

Undefined when x = ______Undefined when x = ______

y  2 x 2  5x  6 3) 2 4) y  9y 18 x 2  2x 15

12 p 2  6 p  6 5x 2 10x  75 5) 6) 4( p 1) 2 4x 2  24x  28

6 Algebra 2 Name______HW- Operations with Rational Expressions Date ______

Perform the indicated operations:

7 8 9 10 11 12 13 14 15