Algebra 2 Chapter 5

Factoring

100

Factor:  2x^2-50 

2(x+5)(x-5)

200

Factor:  4x^2-7x-15 

(4x+5)(x-3)

300

Solve by factoring.

x^2-6x+5=0

x=5 or x=1

400

Solve by factoring.

x^2-49

x=7 and x=-7

500

Solve by factoring.

2x^2-20x+42=0

x=7 or x=3

Completing the Square

100

Change the following equation from general form to vertex form by completing the square.

y=x^2+6x-5

y=(x+3)^2-14

200

Change the following equation from general form to vertex form by completing the square.

y=x^2-12x+3

y=(x-6)^2-33

300

Solve by completing the square: 

x^2-2x-24=0

x=-4 or x=6

400

Solve by completing the square:

x^2+6x-91=0

x=7 or x=-13

500

Solve by completing the square:

x^2-8x-16=0

x=4+-4sqrt(2)

Quadratic Formula

100

Find the discriminant:  x^2-2x+8=0 

What type of solutions will we have?

Discriminant: -28

Type: 2 complex solutions

200

Find the discriminant:  2x^2-x-6=0 

What type of solutions will we have?

Discriminant: 49

Type: 2 real solutions

300

Solve the following quadratic equation by using the quadratic formula:

x^2+6x+5=0

x=-1 or x=-5

400

Solve the following quadratic equation by using the quadratic formula:

x^2+4x+5=0

x=-2+-i

500

Solve the following quadratic equation by using the quadratic formula:

x^2+4x+7=0

x=-2+-isqrt(3)

Rational Expressions

100

Simplify the rational expression:

((x-3)(x+4))/((x+4)(x-2))

(x-3)/(x-2)

200

Simplify the rational expression:

(x^2-9)/(x^2+2x-15)

(x+3)/(x+5)

300

Simplify the rational expression:

(x^2-5x-6)/(x^2+x-42)

(x+1)/(x+7)

400

Simplify the rational expression:

(2x+6)/(x^2-9)

2/(x-3)

500

Simplify the rational expression:

(3x^2-75)/(2x^2-7x-15)

(3(x+5))/(2x+3)

Random

100

Solve for x:

(x+1)(x-3)=0

x=-1 and x=3

200

Simplify the root: 

sqrt(80)

4sqrt(5)

300

Write the factored form of the equation: 

y=x^2-7x-60

What are the x-intercepts? (write as ordered pairs)

(-5,0) and (12,0)

400

Solve.

2(x+1)^2-72=0

x=5 and x=-7

500

Solve.

 3(x-1)^2+27=0 

x=1+-3i