# How do you use synthetic division to find the x intercepts of g(x)=x^3 -3x +2?

Nov 30, 2015

You want to look for values of x such that g(x) = 0, then (x, 0) will be an x-intercept. If you divide g(x) by x - c, the remainder will be g(c).

#### Explanation:

We only need to try c = ±1, ±2 because the c needs to go into the constant term 2 of g(x). Trying c = 1 means look if x - 1 is a factor.

The coeffs of g(x) are 1, 0, -3, and 2. Try those:

1 ) . 1 . 0. . -3 . 2
. . . . . . 1 . . 1 . -2
---------------------
. . . 1 . 1 . . -2 . 0 . . . the remainder is 0, so g(1) = 0.

This also means (x - 1) is a factor of g(x);
g(x) = (x - 1)*(quotient)

Now the quotient is x^2 + x - 2, so factor that and find the other x-intercepts: (x + 2)(x - 1). Counting the first factor, we have
g(x) = (x - 1)(x + 2)(x - 1) = (x - 1)^2 (x + 2).

So the x-intercepts are x = 1 (twice) and x = -2.

...// dansmath strikes again \\...