<p>The graph of P(x)=3x^5+5x^3-8x+2 can cross the x-axis in no more than r points. what is the value of r?</p>
<p>I thought the value of r (which is the number of zeros) was 5 because "every polynomial of degree n has exactly n zeros."</p>
<p>The answer however is 3 because of descartes rule. Which one should I normally apply? to find the number of zeros?</p>
<p>because it is a fifth degree polonomial, there are AT MOST 5 zeros. Descartes rule of signs will narrow it down to how many there actually are. so basically, go with descartes.</p>
<p>well, i don't know if i'm being too pragmatic, but on the sat ii you can use your calculator. which i would most def do on this problem. but i guess if you actually want to learn the material (bleh) then go right ahead and learn the slight nuances in the precal theorems. (which i have never found to be useful anywhere)</p>
<p>but again yaaaayyy for practicality.</p>
<p>yes, just solve for x with P(x) = 0 and count the solutions :)</p>
<p>or graph the function and count the intersections with the x-axis</p>