Polynomial Inequalities

Key Questions

  • They forget to flip the sign of the inequality when they multiply or divide by a negative number.

  • I use what is called the "test point method" to solve polynomial inequalities.

    Ex: (x-3)(x+2) > 0

    The factors on the left and the 0 on the right should remind you of the Zero Product Property. In this inequality, we are looking for products that are positive, and not equal to zero.

    Since the values of x = 3 and x = -2 both produce zeros, I put those onto a number line and leave open circles to mean that they are not included in the solution set.

    my number line 1

    Next, test values between and on the outsides of these two points to see if you get a true statement:

    Ex: test -3 (-3-3)(-3+2) = negative times negative = positive (TRUE)

    Ex: test 0 (0-3)(0+2) = negative times positive = negative (FALSE)

    Ex: test 4 (4-3)(4+2) = positive times positive = positive (TRUE)

    and shade your number line accordingly:
    my number line 2

    Last, I have my students write their solution sets in interval notation.

    The above process will be the same for polynomials of larger degree and more factors. Find a tough one and try it!