Algebra 2 Christmas Review

Solving Equations or Inequalities

100

6-x=2x+9

x=-1

200

1/2x-4= 3/4x

x=-16

300

abs(2x+3)=5

x=1, -4

400

4x^3-8x^2=0

x=0, 2

500

abs(2x-3)>7

x>5 or x<-2

Quadratics

100

(3-2i)(5-6i)=

3-28i

200

Solve using the quadratic formula.

 2x^2-5x-3=0 

x=3, -1/2

300

What number do you add to complete the square?

x^2-20x

100

400

(3x-2)^2=4

x=0, 4/3

500

x^2=-8x

x=0, -8

Polynomials

100

Write the polynomial in standard form and state its degree.

-3x^5+2x^4-5x^3+x^2+8x-9

5

200

(x-7)(2x+9)

2 x^2-5x-63

300

Divide  (4x^3-3x^2+x+1)div(x+2) 

4x^2-11x+23

remainder -45

400

List the potential rational zeros of the function.

 f(x)=6x^4+2x^3-x^2+20 

+-{1, 2, 4, 5, 10, 20, 1/2, 5/2, 1/3, 2/3, 4/3,5/3, 10/3, 20/3, 1/6, 5/6}

500

Find the real zeros of the function.  

 f(x)=x^3-5x^2-2x+24 given 4 is a zero.  

x=-2, 3

Absolute Value

100

abs(3x-1)=2

x=1, -1/3

200

abs(1-4x)=5

x=-1, 2/3

300

abs(4x+10)<14

-6<x<1

400

 abs(4x-9)>27 

x>9, x<-9/2

500

abs(3-9x)>60

x>7 or x<57/-9 

Factoring

100

 12a^2b^2-3ab 

3ab(4ab-1)

200

x^2-6x-16

(x-8)(x+2)

300

2-8x^2

2(1-2x)(1+2x)

400

3x^2+10x-8

(3x-2)(x+4)

500

5x^2-22x-15

(x-5)(5x+3)