 In this video, I provide the solution to question number 9 for practice exam number 3 from math 1050. We have to solve the polynomial inequality x minus 1 squared times x plus 4 is greater than 0. So if we think of the left-hand side as the function f of x right here, we're essentially trying to graph this thing. Graphing is really the best way to solve these inequalities here. And so let's just sketch a graph of this thing really quickly. Because the left-hand side is already factored, we can see the x-intercepts. These are the markers for our inequality here. We're going to have x as 1 comes from the first one. And then we have negative 4 from the second one. Looking at the multiplicities, x minus 1 has a even multiplicity. So we're going to touch the x-axis right there. x plus 4 has an odd multiplicity. So we're going to cross the x-axis there. This function is approximately equal to x cubed as x goes to plus or minus infinity. So the in-behavior would point up on the right-hand side and points down on the left-hand side. And so putting this information together, we have to get a picture that looks something like this. So now the thing we're looking for is what happens above the x-axis. So we want f of x to be greater than 0. That means we're looking for things above the x-axis. So that happens here from negative 4 to 1. And it also happens from 1 to infinity. f of x is not greater than 0 at negative 4 at 1 because at those x-intercepts f of x is equal to 0. So we see that the correct answer is going to be negative 4 to 1, union 1 to infinity. So the correct answer is c.