Devin's Reflection

Rational Root therom

Example: f(x)= 2x^3 + 3x^2 - 8 + 3

Step 1: find all possible roots..

p: factors of 3: 1, -1, 3, -3
q: factors of 2: 1, -1, 2, -2

*p is the leading constant term & q is the leading coefficient

possible roots are (p/q): 1, -1, 1/2, -1/2, 3, -3, 3/2, -3/2

Step 2: now you can plug all of the possible roots in your calculator to find the roots that work

• the zero will be: 1, 1/2, -3

Step 3: use synthetic division to factor all of the roots that work

you should get: (x - 1) (2x^2 + 5x + 3)

Step 4: slove further

(this can be factored...)

= (x - 1) (2x^2 + 5x + 3)

= (x - 1) (2x - 1) (x + 3)

(set x = 0 )

x = 1, 1/2, -3