College Algebra Key Concepts

Distributing

100

5(x+5)

5x+25

200

3(11x+4)

33x+12

300

6x(x+9)

6x²+54x

400

(x+25)(x+3)

x²+28x+75

500

(2x+3)(12x+1)

24x²+38x+3

Factoring

100

w³ + 4w

w(w² + 4)

200

2x² - 2x - 24 = 0

x₁ = -3, x₂ = 4

300

4a² - 12a + 8

4(x-1)(x-2)

400

10x² + 16x + 6

2(x+1)(5x+3)

500

9x⁴ - 18x² + 21x

3x(3x² - 6x +7)

Simplifying

100

X+3+2 Simplify the equation

X+5

200

X^2+2x+3+8 Simplify this equation

X^2+2x+11

300

5x-2+2x+5 Simplify this

7x+3

400

2x^2 -x^2 +x+3x Simplify

x^2+4x

500

3x^3+2-2x^2+5x-3x^2-x Simplify this equation

3x^3-5x^2 +4x+2

Graphing

100

(9/3x)-2

Y-intercept at (0,-2)

Point at (1,1)

200

4y+3=8x+15

y=2x+3

Y-intercept at (0,3)

Point at (1,5)

300

7y+16=5x+51

y=(5/7x)+5

Y-intercept at (0,5)

Point at (-4,0)

400

4y+2x-16

y=(-1/2x)+4

Y-intercept at (0,4)

Point at (2,3)

500

7y+6x-3=10x-3y-13

y=(2/5x)-1

Y-intercept at (0,-1)

Point at (10,1)

Tranformations

100

f(x)=x²+2

Move the line UP 2 units 

200

f(x)=(x-1)-1

Move the line RIGHT 1 unit and DOWN 1 unit

300

f(x)=4^-x

Reflect the line across the Y-AXIS

400

f(x)=-4^x

Reflect the line across the X-AXIS

500

f(x)=-2^-x+3+2

Reflect the line across the X-AXIS, then reflect it across the Y-AXIS. Move the line LEFT 3 units and UP 2 units