Glossary for Lesson 12: Quadratic and Rational Inequalities

Difference of Squares

A difference of squares is a polynomial formed by subtracting one perfect square from another.  In other words, it is an expression of the form a^2-b^2.  This can be factored as follows: a^2-b^2=(a-b)(a+b) .

Rational Expression

A rational expression is the ratio of one polynomial to another.  Thus, a rational expression is anything that can be written as \frac {p}{q} , where p and q are both polynomials and q is not 0

Critical Value

When solving a polynomial inequality or a rational inequality, critical numbers or critical values are values that divide the number line into test intervals, intervals in which we know the inequality will be either true for every value contained in the interval or not true for any value in it.
We can find the critical numbers for a polynomial inequality by simply finding the x -coordinates of the x -intercepts.  If we rearrange a rational inequality so that one side of the inequality is equal to 0 and the other side is just a rational expression, the critical numbers will be values of x that make either the numerator or the denominator of the rational expression equal to 0 .