The points are arranged so that from left to right, the first one is below the x-axis, the second is above the x-axis, the third is below the x-axis, the fourth is above the x-axis, etc. If you plot 3 points like this, you need to cross the x-axis twice, meaning the degree is at least 2. If you plot 4 points like this, you need to cross the x-axis 3 times, meaning the degree is at least 3. Plot 5 points, and you need to cross the x-axis 4 times. Do you see the pattern? It looks like if you plot 40 points, you need to cross the x-axis 40-1=39 times. The degree is the number of times you cross the x-axis, in this extreme case. Then the answer to your question is 39. Since this is an extreme case, then degree 39 guarantees all other possible arrangements of 40 points. Is this an on-line exercise? If so, try entering 39 for the answer and see if it accepts it.