Question 145724: What is a rational zero of this formula and how do you use it to find all zero's of the funtion? 2x^3-x^2-12x+6 Answer by rapaljer(4671) (Show Source):
You can put this solution on YOUR website! For this particular problem, you can factor by grouping. Group the first two and last two terms:
2x^3-x^2-12x+6
x^2(2x-1)-6(2x-1)
Take out the common factor of (2x-1)
(2x-1)(x^2-6)
Set each factor equal to zero:
2x-1=0
2x=1
x=1/2
The second factor has NO rational roots, since
x^2-6=0
x^2=6 and
The only RATIONAL ROOT is x=1/2.
For additional help please see my website by clicking on my tutor name "rapaljer" anywhere in algebra.com. Look for the "MATH IN LIVING COLOR" pages and select College Algebra. See Chapter 3.04 Factoring by Synthetic Division. Other sections from Chapter 3 may also be of interest to you and relevant. This material was written to be understood by students who have trouble with math.
