standard_description: Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x – a is p(a), so p(a) = 0 if and only if (x – a) is a factor of p(x).
problem_activity: Problem 1
Mr. Schaut measured the height of all of the sunflower plants in his garden. The data are shown in the table below.
| **           Heights of Sunflower Plants (in inches)          ** |                   |                   |                   |                   |
|------------------------------------------------------------------|-------------------|-------------------|-------------------|-------------------|
|                        $$60\frac{1}{2}$$                         | $$61\frac{1}{2}$$ |      $$61$$       | $$60\frac{1}{2}$$ | $$61\frac{1}{4}$$ |
|                        $$60\frac{3}{4}$$                         | $$60\frac{3}{4}$$ | $$60\frac{3}{4}$$ |      $$61$$       |      $$60$$       |
|                              $$62$$                              |      $$61$$       | $$60\frac{1}{4}$$ |      $$61$$       | $$60\frac{1}{2}$$ |
|                        $$61\frac{1}{2}$$                         | $$61\frac{1}{4}$$ | $$61\frac{1}{4}$$ |      $$62$$       | $$61\frac{1}{4}$$ |
|                        $$61\frac{1}{4}$$                         | $$61\frac{3}{4}$$ | $$61\frac{1}{2}$$ | $$61\frac{1}{4}$$ | $$61\frac{1}{2}$$ |
|                              $$61$$                              | $$61\frac{1}{4}$$ | $$61\frac{3}{4}$$ | $$61\frac{1}{2}$$ | $$60\frac{1}{4}$$ |
a.   Make a dot plot of Mr. Schaut’s data. Remember to label all parts of your dot plot.
b.   Answer the following questions based on the data.
How many plants were measured in all?
What are the three most frequent measurements in order from shortest to tallest? How many plants were one of those three heights?
What is the typical height of a sunflower in Mr. Schaut’s garden? Justify your reasoning.
Problem 2
a.   Create a dot plot using just the first three rows of data from Anchor Task #1, copied below. Remember to label all parts of your dot plot.
| **                Heights of Sunflower Plants (in inches)               ** |                   |                   |                   |                   |
|----------------------------------------------------------------------------|-------------------|-------------------|-------------------|-------------------|
|                             $$60\frac{1}{2}$$                              | $$61\frac{1}{2}$$ |      $$61$$       | $$60\frac{1}{2}$$ | $$61\frac{1}{4}$$ |
|                             $$60\frac{3}{4}$$                              | $$60\frac{3}{4}$$ | $$60\frac{3}{4}$$ |      $$61$$       |      $$60$$       |
|                                   $$62$$                                   |      $$61$$       | $$60\frac{1}{4}$$ |      $$61$$       | $$60\frac{1}{2}$$ |
b.   In what ways does this subset of data change the answers to the following questions:
How many plants were measured in all?
What are the three most frequent measurements in order from shortest to tallest? How many plants were one of those three heights?
What is the most typical height of a sunflower?


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