Posted by Vincent on .
Find all the zeros of the function and write the polynomial as a product of linear factors.
g(x)=3x^34x^2+8x+8
On my graphing calculator it says that it is 2/3. But when I do it by hand using synthetic division, I don't get a zero. I'm going crazy here... I've tried 2/3 and 2/3 none of them work... But when I look on my graphing calculator it says that it is 2/3. Help?

Algebra2/Trig 
Reiny,
if x= 2/3 then one of the factors is 3x+2
I did algebraic long division and got x^2  2x + 4 with no remainder.
so g(x)=3x^34x^2+8x+8
= (3x+2)(x^22x+4)
so x= 2/3 or x = 1 ± √3 wich are complex numbers
you will not be able to express it as a product of only linear factors, but rather as a
product of a linear factor times a quadratic factor
BTW, I did get a zero when doing synthetic division.
(2/3) │ 3 4 8 8
********** 2 4 8
******** 3 6 12 0