Posted by Rose on Saturday, September 8, 2012 at 8:37pm.
Can someone show me the steps for how to solve:
1.) f(x) = 4x^4 3x^3 +2x^2 +x3
2.) f(x) = x^3  2x^2 5x +6
3.) f(x) = 3x^3 2x^2 + x 1
Thank you so much :)

For what x ?  Damon, Saturday, September 8, 2012 at 8:42pm
You only typed half the problem. Perhaps you are supposed to graph, not solve?

Math  Rose, Saturday, September 8, 2012 at 9:09pm
sorry, i forgot to say the instructions said "find all possible rational roots"

Math  Damon, Saturday, September 8, 2012 at 9:23pm
Result:
The roots of the polynomial 4x4  3x3 + 2x2 + x  3 are:
X1 = 0.301 + 1.002*i
X2 = 0.301  1.002*i
X3 = 0.905
X4 = 0.757 
Math  Damon, Saturday, September 8, 2012 at 9:24pm
That is from:
http://www.mathportal.org/calculators/polynomialssolvers/polynomialrootscalculator.php 
Math  Damon, Saturday, September 8, 2012 at 9:26pm
As you can see you really have to graph that polynomial to find the roots. If you have a graphing calculator, try that
Notice that it only crosses the x axis twice and then has a complex pair for the third and fourth roots 
Math  Damon, Saturday, September 8, 2012 at 9:27pm
For the second one you can see that one is a root by inspection.
Then you can divide by (x1) to get a quadratic which you can solve. 
Math  Damon, Saturday, September 8, 2012 at 9:42pm
By the way if you tried all possible rational roots results on the first problem using factors of the first and last term 3 and 4 ( 3, 2, 4) you would have found that it has no rational factors by the rational root test.

Math  Rose, Sunday, September 9, 2012 at 12:12am
thank you so much for your help ! :)