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?

:)

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- Sep 17th 2009, 07:55 AMtsmithHow 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?

:) - Sep 17th 2009, 08:03 AMmathaddict

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 $ - Sep 17th 2009, 04:18 PMpacman
[I]factor: x^3 + 11x^2 + 39x + 29 = (x + 1)(x^2 + 10x + 29) = (x + 1)(x + (5 - 2i))(x + (5 + 2i))