Activity 2: Write the resulting polynomial. 1. Add 7 − 2 to 3 + 4. 2. What is the sum of 2 + 5 − 2 and 8 − 7? 3. Add 4 + 2 − 3 2 to 2 2 + 5 + 5. 4. What is the sum when 2 + − 3 is added to the sum of 2 2 − 3 + 4 and 3 2 − 3? 5. What is the sum when 4 2 − 4 + 7 is added to the sum of −3 2 − 6 + 5 and 6 2 + 5 − 7? 6. What is the sum when 4 2 + 5 − 8 is added to the sum of −3 2 − 8 + 2 and −5 2 − 9 − 2? 7. What must be added to 3 − 1 to obtain 0? 8. What must be added to 5 + 6 to obtain 2 + 10?

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Activity 2: Write the resulting polynomial. 1. Add 7 − 2 to 3 + 4. 2. What is the sum of 2 + 5 − 2 and 8 − 7? 3. Add 4 + 2 − 3 2 to 2 2 + 5 + 5. 4. What is the sum when 2 + − 3 is added to the sum of 2 2 − 3 + 4 and 3 2 − 3? 5. What is the sum when 4 2 − 4 + 7 is added to the sum of −3 2 − 6 + 5 and 6 2 + 5 − 7? 6. What is the sum when 4 2 + 5 − 8 is added to the sum of −3 2 − 8 + 2 and −5 2 − 9 − 2? 7. What must be added to 3 − 1 to obtain 0? 8. What must be added to 5 + 6 to obtain 2 + 10?

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SHALLOMDAVEGO SHALLOMDAVEGO · Answer 1

Answer:

There are 10!/(4!(10-4)!) = 210 such combinations assuming no

repeats are allowed:

{0, 1, 2, 3}, {0, 1, 2, 4}, {0, 1, 2, 5}, {0, 1, 2, 6}, {0, 1,

2, 7}, {0, 1, 2, 8}, {0, 1, 2, 9}, {0, 1, 3, 4}, {0, 1, 3, 5},

{0, 1, 3, 6}, {0, 1, 3, 7}, {0, 1, 3, 8}, {0, 1, 3, 9}, {0, 1,

4, 5}, {0, 1, 4, 6}, {0, 1, 4, 7}, {0, 1, 4, 8}, {0, 1, 4, 9},

{0, 1, 5, 6}, {0, 1, 5, 7}, {0, 1, 5, 8}, {0, 1, 5, 9}, {0, 1,

6, 7}, {0, 1, 6, 8}, {0, 1, 6, 9}, {0, 1, 7, 8}, {0, 1, 7, 9},

{0, 1, 8, 9}, {0, 2, 3, 4}, {0, 2, 3, 5}, {0, 2, 3, 6}, {0, 2,

3, 7}, {0, 2, 3, 8}, {0, 2, 3, 9}, {0, 2, 4, 5}, {0, 2, 4, 6},

{0, 2, 4, 7}, {0, 2, 4, 8}, {0, 2, 4, 9}, {0, 2, 5, 6}, {0, 2,

5, 7}, {0, 2, 5, 8}, {0, 2, 5, 9}, {0, 2, 6, 7}, {0, 2, 6, 8},

{0, 2, 6, 9}, {0, 2, 7, 8}, {0, 2, 7, 9}, {0, 2, 8, 9}, {0, 3,

4, 5}, {0, 3, 4, 6}, {0, 3, 4, 7}, {0, 3, 4, 8}, {0, 3, 4, 9},

{0, 3, 5, 6}, {0, 3, 5, 7}, {0, 3, 5, 8}, {0, 3, 5, 9}, {0, 3,

6, 7}, {0, 3, 6, 8}, {0, 3, 6, 9}, {0, 3, 7, 8}, {0, 3, 7, 9},

{0, 3, 8, 9}, {0, 4, 5, 6}, {0, 4, 5, 7}, {0, 4, 5, 8}, {0, 4,

5, 9}, {0, 4, 6, 7}, {0, 4, 6, 8}, {0, 4, 6, 9}, {0, 4, 7, 8},

{0, 4, 7, 9}, {0, 4, 8, 9}, {0, 5, 6, 7}, {0, 5, 6, 8}, {0, 5,

6, 9}, {0, 5, 7, 8}, {0, 5, 7, 9}, {0, 5, 8, 9}, {0, 6, 7, 8},

{0, 6, 7, 9}, {0, 6, 8, 9}, {0, 7, 8, 9}, {1, 2, 3, 4}, {1, 2,

3, 5}, {1, 2, 3, 6}, {1, 2, 3, 7}, {1, 2, 3, 8}, {1, 2, 3, 9},

{1, 2, 4, 5}, {1, 2, 4, 6}, {1, 2, 4, 7}, {1, 2, 4, 8}, {1, 2,

4, 9}, {1, 2, 5, 6}, {1, 2, 5, 7}, {1, 2, 5, 8}, {1, 2, 5, 9},

{1,2, 6, 7}, {1, 2, 6, 8}, {1, 2, 6, 9}, {1, 2, 7, 8}, {1, 2, 7,

9}, {1, 2, 8, 9}, {1, 3, 4, 5}, {1, 3, 4, 6}, {1, 3, 4, 7},

{1, 3, 4, 8}, {1, 3, 4, 9}, {1, 3, 5, 6}, {1, 3, 5, 7}, {1, 3,

5, 8}, {1, 3, 5, 9}, {1, 3, 6, 7}, {1, 3, 6, 8}, {1, 3, 6, 9},

{1, 3, 7, 8}, {1, 3, 7, 9}, {1, 3, 8, 9}, {1, 4, 5, 6}, {1, 4,

5, 7}, {1, 4, 5, 8}, {1, 4, 5, 9}, {1, 4, 6, 7}, {1, 4, 6, 8},

{1, 4, 6, 9}, {1, 4, 7, 8}, {1, 4, 7, 9}, {1, 4, 8, 9}, {1, 5,

6, 7}, {1, 5, 6, 8}, {1, 5, 6, 9}, {1, 5, 7, 8}, {1, 5, 7, 9},

{1, 5, 8, 9}, {1, 6, 7, 8}, {1, 6, 7, 9}, {1, 6, 8, 9}, {1, 7,

8, 9}, {2, 3, 4, 5}, {2, 3, 4, 6}, {2, 3, 4, 7}, {2, 3, 4, 8},

{2, 3, 4, 9}, {2, 3, 5, 6}, {2, 3, 5, 7}, {2, 3, 5, 8}, {2, 3,

5, 9}, {2, 3, 6, 7}, {2, 3, 6, 8}, {2, 3, 6, 9}, {2, 3, 7, 8},

{2, 3, 7, 9}, {2, 3, 8, 9}, {2, 4, 5, 6}, {2, 4, 5, 7}, {2, 4,

5, 8}, {2, 4, 5, 9}, {2, 4, 6, 7}, {2, 4, 6, 8}, {2, 4, 6, 9},

{2, 4, 7, 8}, {2, 4, 7, 9}, {2, 4, 8, 9}, {2, 5, 6, 7}, {2, 5,

6, 8}, {2, 5, 6, 9}, {2, 5, 7, 8}, {2, 5, 7, 9}, {2, 5, 8, 9},

{2, 6, 7, 8}, {2, 6, 7, 9}, {2, 6, 8, 9}, {2, 7, 8, 9}, {3, 4,

5, 6}, {3, 4, 5, 7}, {3, 4, 5, 8}, {3, 4, 5, 9}, {3, 4, 6, 7},

{3, 4, 6, 8}, {3, 4, 6, 9}, {3, 4, 7, 8}, {3, 4, 7, 9}, {3, 4,

8, 9}, {3, 5, 6, 7}, {3, 5, 6, 8}, {3, 5, 6, 9}, {3, 5, 7, 8},

{3, 5, 7, 9}, {3, 5, 8, 9}, {3, 6, 7, 8}, {3, 6, 7, 9}, {3, 6,

8, 9}, {3, 7, 8, 9}, {4, 5, 6, 7}, {4, 5, 6, 8}, {4, 5, 6, 9},

{4, 5, 7, 8}, {4, 5, 7, 9}, {4, 5, 8, 9}, {4, 6, 7, 8}, {4, 6,

7, 9}, {4, 6, 8, 9}, {4, 7, 8, 9}, {5, 6, 7, 8}, {5, 6, 7, 9},

{5, 6, 8, 9}, {5, 7, 8, 9}, {6, 7, 8, 9}

If repeats are allowed, the number increases to 715 combinations

I'll leave it as an exercise for the reader to list the extra 505

combinations.