Algebra 2 Units 1-3 Concepts

Operations of Complex Numbers

100

Add the Complex Numbers:

(6+18i)+(-5-2i)

1+16i

200

Subtract the Complex Numbers

(5-6i)-(3-2i)

2-4i

300

Multiply:

(4+i)(7-3i)

31-5i

400

(7-3i)²

40-42i

500

Divide:

1+2i/7+2i

11+12i/53

Quadratics

100

2x² +3x+1=0

Solve using the Quadratic Formula

-1/2 and -1

200

(x-2)²=49

Use the Square Root Method to solve.

x=9, x=-5

300

Factor:

x²-13x+22=0

x=2, x=11

400

Factor:

3a+11a+6=0

a=-3, a=-2/3

500

Solve by using Completing the Square:

2x²+4x+38=-6

x=-1±i√21

Operations of Polynomials

100

(4x-2y)+(-2x+6y)

2x+4y

200

(6x²+3x-5)-(4x²-2x+3)

2x²+5x-8

300

Multiply.

(4x-3)(5x-12)

20x²-63x+36

400

Solve using the Area Model.

(3x²-2x+7)(-10x²+4x+1)

-30x⁴+32x³-75x²+26x+7

500

Use Synthetic Division to solve.

(x⁴-1)/(x+1)

x³-x²+x-1

Binomial Expansion

100

(x+2y)³

x³+6x²y+12xy²+8y³

200

(b+4)⁵

b⁵+20b⁴+160b³+640b²+1280b+1024

300

(x-2y)⁶

x⁶-12x⁵y+60x⁴y²-160x³y³+240x²y⁴-192xy⁵+64y⁶

400

(2y-x)⁷

128y-448y⁶x+672y⁵x²-560y⁴x³+280y³x⁴-84y²x⁵+14yx⁶-x⁷

500

(x⁴-y)⁵

x²⁰-5x¹⁶y+10x¹²y²-10x⁸y³+5x⁴y⁴-y⁵

Rational Root Theorem

100

f(x)=x³+x²-17x+15

Final Roots: 1,3,-5

200

f(x)=2x³-3x²-11x+6

Final Roots: -2, 3, 1/2

300

f(x)=x³-x²-34x-56

Final Roots: -2, 7, -4

400

f(x)=3x³-4x²-17x+6

Final Roots: -2, 3, 1/3

500

f(x)=x⁴-x³-12x²-2x+8

Final Roots: -1, 4, -2±√12/2