Exam I

Question 1

121 = 100y^2 - What do you see?

Answer 1

I see the Final Steps
Switch sides
100y^2 = 121

Divide both sides by 100

y^2 = 121/100
Take the square root of both sides
y = +/- 11/10

Question 2

• 6z + 1 = 2z^2 + z + 6 What do you see?

Answer 2

A binomial and a polynomial 
I need to combine like terms
Switch sides
Subtract 1 from both sides
Add 6z to both sides
2z^2 +7z + 5         2X5 = 10    2+5 = 7
2z^2 + 2z + 5z + 5
2z (z + 1)  5 (z + 1)
z + 1 = 0          2z + 5 = 0
z = -1                2z = -5
                         z   =  -5/2

Question 3

(y - 2) (y^2 - 2y + 4) What do you see?

Answer 3

Multiply y by everything in second parenthesis
Multiply -2 by everything in second parenthesis
Combine like terms

Question 4

(w - 3)^2 = 16w^2 - 14w + 10 What do you see?

Answer 4

I need to multiply (w -3) (w-3)

Combine like terms

Question 5

y^2 - 36 What do you see?

Answer 5

Difference of squares
(y + 6) (y - 6)

If the problem was y^2 + 36 could you do the same thing?

Question 6

9z^2 + z + 8 What do you see?

Answer 6

prime

Question 7

x^2 - 51 What do you see?

Answer 7

prime

Question 8

18w^2 - 54w + 40 What do you see

Answer 8

Factor out a common term
2 (9w^2 - 27w +20)
Do not forget to go back and get your 2 when you complete your calculations.

Question 9

m + n = p, what must p equal?

Answer 9

0

Question 10

(x - 4) ( x + 5) = 0 What do you see?

How would you solve?

Answer 10

x - 4 = 0 x + 5 = 0

x = 4 x = -5

Question 11

0 = (3z - 1) (z - 5) What do you see?

How would you solve?

Answer 11

3z - 1 = 0 z - 5 = 0
3z = 1 z = 5
z = 1/3

Question 12

-12y^2 = 30y What do you see?

Answer 12

It is not a perfect square
My negative sign (-) needs to be factored out
I can subtract 30y from both sides
Then I can factor out a 6 and my negative sign (-)
-12y^2 - 30y = 0
-6y (2y + 5) = 0
Solve for y

-6y = 0             2y + 5 = 0
y = 0/-6                  2y = -5
y = 0                         y = -5/2

Question 13

-2y^2 = 5y What do you see

Answer 13

Subtract 5y
The negative sign needs to be factored out

• 2y^2 - 5y = 0
• y (2y + 5) = 0

Question 13

-2y^2 = 5y What do you see

Answer 13

Subtract 5y
The negative sign needs to be factored out

• 2y^2 - 5y = 0
• y (2y + 5) = 0