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 Depdendent Variable

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 Dependent Variable

 Number of inequalities to solve: 23456789
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To solve inequalities involving polynomials of higher degree, use the fact that a polynomial can change signs only at its real zeros (the numbers that make the polynomial zero). Between two consecutive real zeros, a polynomial must be either entirely positive or entirely negative. This means that when the real zeros of a polynomial are put in order, they divide the real line into test intervals in which the polynomial has no sign changes. Thus, if a polynomial has the factored form

(x - r1)(x - r2)...(x - rn), r1 < r2 < r3 < ... < rn

the test intervals are

(-∞, r1), (r1, r2), ..., (rn-1, rn), and (rn, )

To determine the sign of the polynomial in each test interval, you need to test only one value from the interval.

Example 