What about a 3rd degree polynomial that...
| touches the x-axis 3 times? |
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| touches the x-axis twice? |
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| touches the x-axis once? |
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| never touches the x-axis? | Nope! Since the tails go off in opposite directions. |
YOUR TURN:
Can you draw a 4th degree polynomial that...
touches the x-axis 4 times?
touches the x-axis 3 times?
touches the x-axis 2 times?
touches the x-axis 1 time?
never touches the x-axis?