Algebra 2

Operation of Complex Numbers

100

i¹⁸⁴ is equal to i

false 

200

Add: (3+5i)+(4-2i)

7+3i

300

Subtract: (-2+7i)-(-8+i)

6+6i

400

Multiply: (-9-9i)(8+8i)

-144i

500

Divide: (3+15i)/(9-10i)

(-123+165i)/(181)

Quadratics

100

What method was used to solve this quadratic equation?

(x+72)² = 16

√(x+72)² = √16

x+72 = ±4

    /            \

x+72=-4     x+72=4

  -72  -72       -72  -72

x=-76         x=-68

square root method

200

What would the following step be?

step 1: x² +2x-5= 43

step 2: x² +2x= 48

step 3: x²+2x+1= 48+1

step 4: (x+1)² = 49

step 5: x+1 = 7

Step 6: separate and solve

x+1= 7     x+1=-7

   -1  -1        -1  -1

x=6           x=-8

300

Solve using the square root method:

7x² +3=346

x=7      x=-7

400

Solve by factoring:

x²+11x+18=0

x= -2       x= -9

500

Solve using the quadratic formula:

f(x)= 5x² + 9x-3

x=(-9+√141)/(10)     x=(-9-√141)/(10)

Operations of Polynomials

100

Simplify: 9x-18y+5x

14x-18y

200

Add:

(17x²-9x+1)+(2x²+3x+2)

19x²-6x+3

300

Multiply: (10x+4)(15x-3)

(150x²+30x-12)

400

Multiply: (x+3)(8x²+5x-3)

8x³+29x²+12x-9

500

Divide: (x³-9x²+6x+2)/(x-6)

x²-3x-12-70/(x-6)

Binomial Expansion

100

Fill in the blanks to complete pascal's triangle:

1

1 1

1 2 1

1 _ 3 1

1 4 6 4 1

1 5 _ 10 5 1

1 6 15 _ 15 6 1

1 7 21 35 35 _ 7 1

3, 10, 20, and 21

200

Expand the binomial: (2x+4y)³

8x³+48x²y+96xy²+64y³

300

What is the 3rd coefficient of the expansion?  (3x+7y)⁴

2646

400

Expand the binomial: (2+2a)⁵

32+160a+320a²+320a³+160a⁴+32a⁵

500

What is the last coefficient of the expansion? (1+5a)⁵

3125

Rational Root Theorem

100

-4 is a possible root of x³+2x²-7x+4

True

200

List all of the possible roots:

x³+4x²-x-10

{±1,±2,±5,±10}

300

Find all of the roots:

x³+3x²-14x+8

Roots: {2, (-5+√41)/2, (-5-√41)/2}

400

Identify a,b, and c

x⁴+3x³-3x²-7x+6

a= 1  b= 2  c= -3

500

Find all of the roots

x⁴-4x³+7x²-16x+12

Roots: {1,3,2i,-2i}