Math 21 Unit 4 Test

Zero Product Property

100

If 6abc = 0  what do you know about a, b, and/or c?

One of these factors variable factors (a, b, and/or c) must = 0

200

Solve:  

3x^2 -27=0

x = -3, 3

300

Solve:  

2x^2 -5x=3

x = -1/2, 3

400

Solve:  

5x^3 - 40=0

x = 2

500

Solve:  

2x^2+6=8x 

x = 1, 3

Extract a Square Root

100

Solve:  

x^2 = -9

No real solution (wait for Math 22)

200

Solve:  

8x^2+4=-x^2+40

x = -2, 2

300

Solve:  

3(x-1)^2=48

x = -3, -5

400

4(x+3)^2-7=5

x=-3-sqrt3, -3+sqrt3

500

Solve:  

-4(2x-1)^2+3=6

NO REAL SOLUTION

Quadratic Formula

100

How does the discriminant determine the number of real solutions in a quadratic equation?

b^2-4ac

> 0 there are 2 real solutions

<0 there are no real solutions

=0 there is one real solution

200

Solve:  

2x^2 -5x+6=0

no real solution

300

Solve:  

2x^2+3=8x

2+sqrt10/2, 2-sqrt10/2

400

Solve:

3x^2-x=5

1/6+sqrt61/6,1/6-sqrt61/6

500

Solve: 

-9x-5=-2x^2

-1/2, 5

Higher degree and radical

100

Solve:  

x^4 - 2x^2 -24

sqrt6, -sqrt6

200

Solve: 

2x^4=32x^2

0, -4, 4

300

Solve: 

2sqrt(x+1)-3=9

x = 35

400

Solve:  

sqrt(2x+9)-x=3

x = 0

500

Solve:  

5∛(x+3)-2=18

x = 61

Rational exponent and | |

100

Simplify 

(-64)^(2/3)

16

200

Solve: 

(x-5)^(2/3)-6=10

x= -59, 69

300

Solve:  

(x+1)^(3/2)+2=10

x = 35

400

Solve:  

|x^2-2x|=-2x+4

x = -2, 2

500

Solve:  

|2x+2|=x^2-6

x = 

-1-sqrt5, 4