Problem Set

Solve the following problems. Distribute and factor when needed.

1. 1. If −4 is a solution for x in the equation x² + kx + 8 = 0, what is k?

   2. If 8 and −4 are the solutions for x, which of the following could be the equation?

      1. x² − 4x − 32 = 0
      2. x² − 4x + 32 = 0
      3. x² + 4x − 12 = 0
      4. x² + 4x + 32 = 0
      5. x² + 4x + 12 = 0

   3. If 16 − y² = 10(4 + y), what is y?

   4. If x² − 10 = −1, what is x?

   5. If x² − 13x = 30, what is x?

   6. If the area of a certain square (expressed in square meters) is added to its perimeter (expressed in meters), the sum is 77. What is the length of a side of the square?

   7. Hugo lies on top of a building, throwing pennies straight down to the street below. The formula for the height in meters, H, that a penny falls is H = Vt + 5t², where V is the original velocity of the penny (how fast Hugo throws it as it leaves his hand in meters per second) and t is equal to the time it takes to hit the ground in seconds. The building is 60 meters high, and Hugo throws the penny down at an initial speed of 20 meters per second. How long does it take for the penny to hit the ground?

   8. 

   9. If x² − 6x − 27 = 0 and y² − 6y − 40 = 0, what is the maximum value of x + y?

   10. If x² − 10x + 25 = 16, what is x?

   11. 	x2 − 2x − 15 = 0
       Quantity A		Quantity B
       x		1

   12. 	x2 − 12x + 36 = 0
       Quantity A		Quantity B
       x		6

   13. 	xy > 0
       Quantity A		Quantity B
       (x + y)2		(x − y)2