Precalculus Problem Help?
f(x) = 3x3 − 13x2 + 17x − 7
Find all zeros and give a complete factorization.
I've tried so many times but I can't get it right. An explanation as well would be appreciated.
Update:As much as A77Y's answer sounds right, it's saying that one's wrong, too.... raaaaah I HATE WebAssign!
Answers & Comments
Verified answer
First plug the function into your calculator and graph it. Then go 2nd table and you will see that when x=1, y=0. From there do synthetic division using 1 since we know it is a factor.
Here is synthetic division.
| 3 -13 17 -7
1 |
|_______3__-10__7___
3 -10 7 0
The 0 we got here also confirms 1 is a factor or "zero"
Where the 0 is, that is the remainder.
So now we have the equation 3x^2 -10x + 7
Use the quadratic formula on this equation to get x=7/3 and x=1
However, when checking back in the original equation 1 works, but 7/3 does not, so the zeros are 1 with a multiplicity of 2 (that just means it is a double root).
Factorization (x-1)(x-1)(x-7/3)