00:01
So in this problem, what we're being asked to do is solve the given polynomial inequality.
00:05
Well, i see we have a quadratic here.
00:07
So what we need to do first is we need to find the zeros, meaning when is this equation equal to zero? well, in order to do this, we can factor.
00:14
Well, i'm going to set up our two binomials.
00:18
And in this case, we're setting it equal to zero because we're trying to find our zeros in this particular case.
00:22
Well, our first terms have to multiply to 4x squared, and our last terms multiply to negative 15, such that their combination will give us 17.
00:31
Well, in this case, for our first terms, what if we started with 4x and x? so now we would try and come up with two numbers that will multiply the negative 15 that will somehow give us this middle number of 17.
00:42
Well, i'm thinking of 5 and 3.
00:44
Let's say the 5 was positive and the 3 was negative.
00:47
Then our middle term would be 20x minus 3x, which is positive 17x.
00:52
Perfect.
00:53
So now that we have our factors, we're going to set them equal to 0.
00:56
So 4x minus 3 could equal to 0 or x plus 5 could equal to 0.
01:01
So now we'll solve both equations.
01:03
So to solve the first, we're going to add three to both sides.
01:06
So 4x will equal to 3, and then we'll divide both sides by 4.
01:09
So that will leave us with x equal to 3 4s.
01:13
Then to solve the second equation, we just subtract 5 from each side of our expression.
01:17
So that will give us x equals negative 5.
01:19
Okay, great.
01:20
So now we have our zeros.
01:22
So what we're going to now do is we're going to set up a sign chart.
01:26
We're going to put both of our values on here.
01:28
So we're going to have negative 5 and 3 4s...