Question

Pre-Calculus help! Will fan and medal!
Use synthetic division to find the zeros of the function:
f(x)=x^3+x^2+4x+4

Answer 1

\[f(x)=x^3+x^2+4x+4\]

Answer 2

Hey there AvocadoChick! :)

You need to apply rational root theorem to find a root before you can apply synthetic division. Our rational root theorem tells us that the factors of 4 will all be possible roots of this polynomial. So we'll have to check each one until we find one that works.

We're looking for a root,
so we're looking for an x-value that gives us a y-value of zero.\[\large\rm 0=x^3+x^2+4x+4\]

Answer 3

There are a few factors of 4,
4*1
-4*-1
2*2
-2*-2

Let's start with 1, that's a nice easy number,
\(\large\rm x=1:\qquad 1^3+1^2+4(1)+4\ne0\)
Hmm that didn't give us zero.
Let's try another factor,
\(\large\rm x=-1:\qquad (-1)^3+(-1)^2+4(-1)+4=0\)

Ooo x=-1 seems to work!
If we take this x=-1 and add 1 to each side, we get,
\(\large\rm x+1=0\)

We found a root!
So we can use the root to apply synthetic division.

Answer 4

Ahh woops, I'm forgetting...
We would use x+1 for `polynomial long division`.
But simply x=-1 for `synthetic division`.

So ignore that last step I applied.