Question

What is 3x^3+2x^2-19x+16 factored?

Answer 1

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

f (x ) = 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

.