# Polynomial Division- Open Middle Problem

Directions: Using the integers 1 to 9, using each number only once, fill in the boxes to create a polynomial and its factor.

What is the other factor?

What patterns do you notice?

Can you expand this to a polynomial of degree 4?

# Logs 2- Open Middle Problem

So this is the problem I am kicking around, I’d like some input on it.

Directions: Using the integers 1 to 9 in the boxes, create a log that satisfies the follow constraints (you can use a number only once):

# Laws of Logs- Open Middle Problem

Directions: Using the integers 0 to 9, fill in the red and blue boxes so that the chart is accurate.  You can only use a number once per red box and once per blue box.

logs are in base 10.

# Logs- Open Middle Problem

Directions: Using the integers 1 to 9, fill in the red and blue boxes so that the chart is accurate.  You can only use a number once per red box and once per blue box.

Thank you to Megan Schmidt, @veganmathbeagle, for introducing me to this graphic from underground mathematics.

Challenge: How would your strategies change if log values had to fit within the interval [0, 1.6)

# Identifying Function Types

Which of these formulas represent a linear relationship?

Explain how you know.

For those formulas that do not form a linear relationship, what type of relationship do they represent?

What would their graph look like?

# Linear Functions?

Which of these formulas represent a linear relationship?

Explain how you know.

# Linear Relationships

List 2 points from a line that satisfies the following (you can use numbers 0-9, but you can only use a number once):

a) Its rate of change must be larger than 2

b) Its y-intercept must be smaller than 3

c) It must share a point with the line described by the rate of change and intercept from a&b

(__,__) and (__,__)

The equation of the two lines is:

y = __x +___

y = __x +___