Select the correct alternative from the given choices. If (x+5)(x+9)(x+3)^2<0, then the solution

step 1 Okay, consider a matrix A in deformation. A equals to y into small x. A here is 3, 1 .5, 1 .5 an

Select the correct alternative from the given choices. If...

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Key Concepts

Polynomial Inequality

A polynomial inequality involves determining the set of x-values for which a polynomial expression is less than, greater than, or equal to zero. This typically involves finding the roots of the polynomial and then analyzing the sign of the polynomial across the resulting intervals.

Critical Points (Zeros)

Critical points are the x-values where the polynomial equals zero and are found by setting each factor of the polynomial to zero. These zeros divide the number line into intervals, which can be tested to see whether the polynomial is positive or negative on those intervals.

Multiplicity of Roots

The multiplicity of a root refers to the number of times that particular solution occurs. Roots with even multiplicity, such as those corresponding to a squared factor, do not change the sign of the expression at that point, whereas roots with odd multiplicity do cause a sign change across the critical point.

Sign Chart Analysis

A sign chart is a useful tool for solving polynomial inequalities. After identifying the critical points, the sign of each polynomial factor is determined in the intervals formed by these points. The overall sign of the polynomial is then derived by considering the product of the signs of the factors in each interval.

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