# Thread: How to find the zeros of this function

1. ## How to find the zeros of this function

Find all the zeros of the function and write the polynomial as a product of linear factors.
f(x) = x^3 + 11x^2 + 39x + 29.

So I think that I might need to use synthetic division, but I'm not sure. The teacher didn't explian this to me. Any help?

2. Originally Posted by tsmith
Find all the zeros of the function and write the polynomial as a product of linear factors.
f(x) = x^3 + 11x^2 + 39x + 29.

So I think that I might need to use synthetic division, but I'm not sure. The teacher didn't explian this to me. Any help?

HI

Factorise f(x) , do you know how ?

$\displaystyle f(x)=(x+1)(x^2+10x+29)$

$\displaystyle x^2+10x+29$ is complex , you can always check its discriminant .

$\displaystyle x+1$ is a factor because $\displaystyle f(-1)=0$

Then you can do the long division to get its quadratic factor .

So the zero of this polynomial would be -1 because -1 makes $\displaystyle f(x)=0$

3. [I]factor: x^3 + 11x^2 + 39x + 29 = (x + 1)(x^2 + 10x + 29) = (x + 1)(x + (5 - 2i))(x + (5 + 2i))