#2**+2 **

f(x) = x^3 - 7x + 6

To find the y intercept, let x = 0 and the y intercept = 6

Note that one of the x intercepts = 1 because

(1)^3 - 7(1) + 6 =

1 - 7 + 6 =

-6 + 6 = 0

So 1 is a root ( an x intercept )

Using synthetic division to find the remaining polynomial

1 [ 1 0 - 7 6 ]

1 1 -6

____________

1 1 -6 0

So....the remaining polynomial is x^2 + 1x - 6.....set to 0 and factor

x^2 + 1x - 6 = 0

(x + 3) ( x - 2) = 0 set each factor to 0 and solve for x and x = -3 and x = 2

And these are the other two x intercepts

Here's the graph : https://www.desmos.com/calculator/e7h0jx35bk

CPhill
Apr 27, 2017