# Polynomial Zero's

I'm have trouble understanding the following problem please assist so I may complete my assignment.

1. Find the real zeros of the function f(x) = -(x + 1)^3 (x - 2)^2 and their corresponding multiplicities. Use the information along with a sign chart (diagram) and then the end behavior to provide a rough sketch of the graph of the polynomial.

2. solve the rational inequality. Express your answer using interval notation.

(3x^2 - 5x - 2) / (x^2 - 9) < 0

© BrainMass Inc. brainmass.com October 10, 2019, 8:09 am ad1c9bdddfhttps://brainmass.com/math/functional-analysis/polynomial-zeros-610505

#### Solution Preview

To find the zeroes you have to set each part of the polynomial equal to zero and solve algebraically. The thing that makes this problem a little easier is thet fact that when either portion of the equation is equal to zero then when it is multiplied by the other is makes the entire equation zero.

Example

f(x)= (x + 2)^2(x-6)^3

split up the equation into 2 equations

0 = (x+2)^2

0 = (x-6)^3

What do we have to do to make the value inside of the parenthesis 0. The fact that we are going to square and cube it is of no consequence because when you square or cube ...

#### Solution Summary

The expert finds zeros of polynomials and graphing with interval notation.