<p>I have some summer homework and can't seem to get this problem:</p>
<p>Finding the x-intercepts of the graph of f (no calculator).
f(x)=4x^3 -3x -1</p>
<p>I've tried factoring, taking the deriv, attempting to square, setting it equal to zero, and the quadratic formula to no avail...</p>
<p>Many thanks in advance! :)</p>
<p>Well, by looking at it, I can tell you that 1 is an answer. Try synthetic division.</p>
<p>Technically, homework help threads are against the rules, though.</p>
<p>Sorry, could you explain how 1 is one of the answers? </p>
<p>All I can see is that -1 is where the y-intercept is.</p>
<p>4(1)^3 - 3(1) - 1 = 0
4 - 3 - 1 = 0</p>
<p>For questions like these (finding the roots of a polynomial that can’t be easily factored), long division and synthetic division are your best options (the latter being the easiest method). Typically, one of the roots will be something in the range of -3 to 3. Just plug these integers in until you find one that is a zero, then use synthetic division.</p>
<p>I would graph it, find one of the solutions of the graph, then use synthetic devision to divide the solution out of the original equation. Then factor.</p>
<p>Oh, good point. Currently trying it out.</p>
<p>Ohhhh now I get it.
Thanks so much PioneerJones and puggly123 :)</p>
<p>Not a problem :)</p>
<p>You’re probably gonna get infracted for posting homework, just FYI.</p>
<p>Is there another place specifically to post problems like these?</p>
<p>nope, you can’t. If synthetic division doesn’t work for you, rational roots is the long, proposed method to use.</p>
<p>^ AHH you beat me to it.</p>
<p>Rational root theorem is the way to go. It’s not even that bad. You’re dealing with 4 and -1. It should be easy seeing as you don’t have many factors to deal with.</p>
<p>dude, how did he beat you to it? MIT was like 25 minutes before you.</p>
<p>Some people post stuff like this in the AP Preparation section, but that’s generally in the spring</p>
<p>^I guess they are working early.</p>