The cubic polynomial is 3x^3 + 2x^2 -19x + 16 \ \

Graph \ \

\ \

The points where it crosses the x axis  will give solutions to the polynimial function . \ \

The graph crosses the x-axis at a point that would suggest a factor. \ \

It crosses the x - axis at one point hence there are one real root. \ \

x = -3.1829

Use synthatic division to detrmine if the given value of x is a root of the polynomial.

\ \

Since f(-3.1829)   =   0,   x   =   -3.1829 is a zero. \ \

The depressed polynomial is  \ \

Since the depressed polynomial of this zero, , is quadratic,

use the Quadratic Formula to find the roots of the related quadratic equation

\ \

Factoring of cubic polynomial is

\ \