# How do you use a graph, synthetic division, and factoring to find all the roots of an equation #x^3 + 5x^2 + 3x -9 = 0#?

##### 1 Answer

Graphing shows us roots

Alternatively, synthetic division and factoring gives us the same roots.

#### Explanation:

Let

The word 'graph' put me off answering this sooner. To plot a graph I usually try to identify turning points, roots, etc first - not the other way round. But if you do plot a graph by picking a few

graph{x^3+5x^2+3x-9 [-10.51, 9.49, -9.56, 0.44]}

Alternatively, first note that the sum of the coefficients is

So

So

Another little trick for recognising this perfect square trinomial is that

So