Algebra II Review

Complex Numbers

100

i⁰ = ?

1

200

√-32 = ?

4√2 i

300

√75 + √-48 = ?

5√3 + 4√3 i

400

i√-293 * √-32 = ?

i (9√3 i) (4√2 i)

500

Find x: 12i/15 = x/4i

-16/5

Quadratics

100

Solve by factoring: x²+2x-24=0

{-4,6}

200

solve by taking square roots: 8x²-4=-32

{-√14/2, √14/2}

300

solve by completing the square: x²-4x+61=-9

{2+√66 i, 2-√66 i}

400

2x²+12x+6=8

{-3+√10, -3-√10}

500

-11x²-7x=9

{-7-√347 i/22, -7+√347 i/22}

Polynomials

100

find # and type of solutions: x²-2x+4=3

1 rational solution

200

find the product: (6x²-8x-6)(7x-7)

42p³-98p²+14p+42

300

expand completely: (y-x)³

y³-3y²x+3yx²-x³

400

solve by synthetic division: (81n⁴-45n³+18n-2) ÷ (-5+9n)

9n³+2n+8/-5+9n

500

solve by long division: (2m⁴+11m³-45m²-65m+12) ÷ (2m-7)

m³+9m²+9m-1+5/2m-7

Comp. of Functions

100

f(x)=6x-2 | g(x)=3x
determine (f+g)(x)

9x-2

200

f(x)=6x-2 | g(x)=3x
determine (f•g)(x)

18x-2

300

h(n)=n+3 | g(n)=-4n+1
find (4h+5g)(9)

-127

400

find the inverse: f(x)=∛x -1

f^-1(x)=(x+1)³

500

State if the given functions are inverses:
f(n)=1/(n-3) | g(n)=1/n +3

yes, f(n) and g(n) are inverses.

Rational Expressions & Equations

100

simplify: 8r²-64r/r-8

8r

200

simplify: x-5/30x+12 + 3/30x+12

x-2/30x+12

300

simplify: 4/5x-3 - 2/4

11-5x/2(5x-3)

400

simplify:
6m³-16m²/2m² * 3m/8-3m

-3m

500

simplify:
7r+1/7r²-27r-4 ÷ 1/r-1

(r-1)/(r-4)