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.

 

test.png

 

What is the other factor?

What patterns do you notice?

Can you expand this to a polynomial of degree 4?

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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.

logs.jpg

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)

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 +___