Polynomial and rational inequalities

steps for a polynomial inequality (6 steps)

1. synthetic division

2. quadratic formula

3. draw graph

4. find ± regions

5. look at orginal formula to see what solutions are

6. write solutions in () or []

close dot vs open dot when do you use for polynomial inequalities

close dot is used for ≥ or ≤

open dot is used for > or <

imaginary number check formula

ax²+bx+c<0 ax²+bx+c <0

a>0 ==> up graph with no solution a<0 ==> down graph with all real #

ax²+bx+c >0 ax²+bx+c >0

a<0 ==> down graph with no solution a>0 ==> up graph with all real #

rational inequality steps (4 steps)

1. must have 0 on one side of the equation

2. simplfy to 1 fraction

3. set numerator and denominator to 0

4. place on number line

note: if you can’t factor use ____ ______

if ____ _____ is imaginary what is the solution

Do you include this in your number line?

quadratic formula

quadratic formula, no solution

no

if its < be sure to…

not include zero