Chapter 5 Test - review

Complex numbers (imaginary)

100

Please simplify:

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

-5 - 9i

200

Please simplify

3 + 3i + 8 - 2i - 7

4 + i

300

Please simplify:

(-2-i)(4+i)

-7 - 6i

400

Please simplify:

(8-6i)(-4-4i)

-56-8i

500

Please simplify:

6(-7+6i)(-4+2i)

96-228i

Completing the square

100

Please solve:

x² - 2x - 3 = 0

x = 3, −1

200

Please solve:

x² + 14x - 38 = 0

-7 ± √87

300

Please solve:

k² − 12k + 23 = 0

k=6 ± √13

400

Please solve:

k² − 4k + 1 = −5

x = 2 ± i√2 

500

Please solve:

b² + 2b = −20

b = −1 ± i √19

Quadratic formula

100

Please solve using the discriminant to tell me how many and what type of solutions you will get:

2x² + 3x − 20 = 0

2 Real solutions

200

Please solve:

m² − 5m − 14 = 0

x = 7, -2

300

Please solve:

b² − 4b + 4 = 0

x = 2

400

Please solve:

2m² − 7m − 13 = −10

Remember, you have to set the equation equal to zero first by adding 10 over from the right side.

 

x=(7±sqrt(73))/4

500

Please solve:

9n² = 4 + 7n

Remember you must move everything over and equal the equation to zero first.

x = (7±sqrt(193))/18

Substitution and Elimination

200

Please solve using substitution or elimination:

y=x² + 5x - 2

y = 3x - 2

(0,-2) and (-2, -8)

300

Please solve using substitution or elimination:

y=-x² - 6x - 6

y = 3

(-3,3)

400

Please solve using substitution or elimination:

y=x² + 2x - 3

y = 2x + 1

(-2,-3)(2,5)

500

Please solve using substitution or elimination:

y=-2x² - 4x - 1

y = 2x + 4

No solution

Polynomial identities

100

Use polynomial identities to solve:

(x+3)²

= x² + 6x + 9

200

Use polynomial identities to solve:

x³ + 64

remember you have to find the cube root of 64 before plugging in your b value!

= (x + 4)(x² - 4x + 16)

300

Use polynomial identities to solve:

x³ - 8

Remember you have to cube root 8 before you can replace your b value into the equation.

=(x - 2)(x² + 2x + 4) 

400

use polynomial identities to solve:

x² - 25 

Remember you have to square root 25 before replacing your b value into the equation.

= (x+5)(x-5)

500

Use polynomial identities to solve:

x³ − 27

(x − 3)(x² + 3x + 9)