Final Exam Review Algebra II

Perfect Cubes / Division

100

Factor x³-64.......

(x-4)(x²+4x+16) 

200

Factor 

8x^3-125

(2x-5)(4x^2+10x+25)

300

(x^3+7x^2 +15x+9) divide (x+1)

x^2 +6x+9

400

(5x^3+8x^2-60)divide(x-2)

5x^2 +18x+36, r 12

500

Solve by factoring 

8x^3 -27=0

x=3/2

x=(-3+-3iroot2(3))/4

Rational Exponents/Square root Functions

100

Simplify 

(x^(1/2)y^(2/3))^(1/4)

x^(1/8)y^(1/6)

200

Solve

root(3)(x+2)-3=0

x=25

300

3(x+1)^(2/3)=12

x=7 or x=-9

400

((16x^14)/(81y^18))^(1/2) 

(4x^7)/(9y^9)

500

root2(x+7)-5=x

x=-3

Functions

100

f(x) = x+1

g(x) = x+2

Fi nd f(x) + g(x)

(f+g)(x) = 2x+3

200

f(x) = x^3+4 

g(x) = x - 5 

F i nd f(x)-g(x)

(f-g)(x) = x^3-x+9

300

f(x) = 8x+3

g(x) = (x+2)^2

F i nd 3f(x)+g(x)

3f(x)+g(x) = x^2 +28x+13

400

f(x) = x-7 

g(x) = x+2

F i nd g(f(x))

g(f(x)) = x-5

500

f(x) = 1/4x^2

g(x) = x^2-7

F i nd f(g(4))

f(g(4)) = 81/4

Log and Natural Logs

100

Condense: log(x+4) - 3logx - logy

log((x+4)/(x^3y))

200

Solve for X:
log₆(2x+5) = 3

x = 211/2 or 105.5

300

(-2)4^x-5 = -17

x= log_4 6

x= 1.29

400

-2log_5(7x)=2

x= 1/35

500

Solve.

lnx - ln9 = 7

x = 9869.6984

x=9e^7

Radical Expressions

100

3sqrt(32)+2sqrt(50)

22sqrt(2)

200

root3(16x^12y^5)

2x^4yroot3(2y^2)

300

sqrt(5)(sqrt(2)-3sqrt(5))

sqrt(10)-15

400

(3sqrt(15))/(5sqrt(12))

(3sqrt(5))/(10)

500

Simplify 

7/(-5+√6)

(-35-7√6)/19