Algebra 2 Final Review

Complex Numbers

100

i² = ?

-1

200

(1+8i)-(-8-4i)+(-4-7i)

5+5i

300

i¹⁷=?

i

400

(6-7i)(-1+4i)

22+31i

500

(-9-6i)/(-5-i)

(51+21i)/26

Factoring

100

In the problem:

4x² + 3x - 11, what are a, b, and c?

a=4, b=3, c=-11

200

Factor: x² + 7x + 6

(x+1)(x+6)

300

Factor: 25x² - 16

(5x+4)(5x-4)

400

Factor: 6x² + 56x + 120

2(3x+10)(x+6)

500

Factor: 27x³ + 64

(3x+4)(9x² -12x + 16)

Function Operations

100

If h(a) = -2a - 5, find h(-7).

9

200

If g(n) = -2n-1 and f(n) = -2n² + 2n, find (g-f)(n).

2n² -4n -1

300

If h(x)= -a + 1 and g(x) = x³ + 2x, find (h * g)(x).

-a⁴ + a³ -2a² + 2a

400

If f(x) = x² - 4x and g(x) = x +3, find (f/g)(x) and state any domain restrictions.

(x² - 4x)/(x+3) where x does not equal -3.

500

If f(x) = -2x-5 and g(x) = x² - x, find f(g(x)).

-2x² + 2x -5

Radicals

100

Simplify: square root (72x²).

6x square root (2)

200

Add:

-3square root(45) + 2square root(5).

-7 square root (5).

300

Simplify:

-square root(20 + 2 square root(8) - square root(20) + 2 square root (8).

-4 square root (5) + 8 square root (2).

400

Simplify:

(4 + square root(2)) * (4 + 3square root(2))

22 + 16 square root (2)

500

Simplify:

5/(2 + square root(3))

10 - 5square root(3)

Random

100

What is the conjugate of 3 + 120i

3-120i

200

What is the degree: 

13x¹³ - 14x⁴⁴ + 8x² - 11x

44

300

If the zeros of a parabola are x = 3 and x = -17, what are the factors?

(x-3)(x+17)

400

If the discriminant is 0, state the type and number of zeros.

1 real zero/solution.

500

Write the formula for a cubic function shifted 3 right and 7 down.

(x-3)³ - 7