Algebra 2 review

Logs

100

rewrite in exponential form:

log₁₁121 = 2

11²=121

200

rewrite in logarithmic form

7³=343

log₇343=3

300

Condense:

4 log₃5-16 log₃12

log₃(5⁴/12¹⁶)

400

Expand: log₇(x³y)²

6 log₇x+2 log₇y

500

Evaluate:

log₂(1/16)

-4

imaginary numbers

100

6(-8+i)-(4i)(-2i)

40-6i

200

-5(5-i)-5(-8-5i)

15+30i

300

(4-10i)/2i

-2i-5

400

(2i)/(5-2i)

(10i-4)/29

500

(7+2i)/(-10-6i)

(-41i+11)/68

functions

100

f(x) = x² +2x

f(5) = 

35

200

h(x) = 2x+2

g(x) = x+2

h+g (x) =

3x+4

300

h(x) = 3x

g(x) = -4x-3

h(g(x)) = 

-12x-9

400

f(x) = -3x

g(x) = x³-5

g(f(x)) = 

-27x³-5

500

g(x) = -2x-5

f(x) = x²-3

f(g(x)) = 

4x²+20x+22

synthetic division

100

(x³+10x²+22x+46)/(x+8)

x²+2x+6 R-2

200

(x³+14x²+53x+69)/(x+9)

x²+5x+8 R -3

300

(x³-11x²+27x-88) /(x-9)

x²-2x+9 R -7

400

(3x³-11x²-24x+18)/(x-5)

3x²+4x-4 R-2

500

(x³-3x²-x+8)/(x+1)

x²-4x+3 R5

factoring

100

FOIL: (x-7)(4x-6)

4x²-34x+42

200

Factor: x²+2x-3

(x-1)(x+3)

300

Factor: x²-100

(x+10)(x-10)

400

Factor: 2x²+11x-6

(2x-1)(x+6)

500

Factor: 30x²-108x+54

6(5x-3)(x-3)