How do you factor #x^3-8x^2+19x-12#?
We have the polynomial
#color(red)(p(x) = x^3-8x^2+19x-12#
As the degree of the polynomial is greater than 2, we need to use Synthetic Division to factorize it.
In Synthetic Division, we first find a value of
#x#that makes this polynomial equal to zero. That is, we need to find the ZERO of the polynomial. We do that by Trial and Error.
#x=color(blue)1#, this Polynomial will equal zero.
- To find the other two factors, we use the process of Synthetic Division. To explain the entire process of Synthetic Division using text is a bit difficult, but this image should help:
The 1, -7 and 12 give us another factor of the polynomial:
We have reduced p(x) to
So finally, we get