00:01
All right, so we have a few questions to solve here.
00:02
So let's start with the first one.
00:04
So in factoring this, we want to find two numbers that multiply to 24 and add or subtract two.
00:11
So we take the numbers that can multiply 24, one times 24, two times 12, three times eight, and four times six.
00:26
Looking at each one of these pairings, we see that four and six can give us the positive two.
00:32
So we want to set it up now how using 4 and 6 we could get the positive 2 well we would need a a positive or i'm sorry a positive 6 and negative 4 solving both of these we say each one of them equal to 0 so we get that x is equal to negative 6 and x is equal to 4 so that is it for that problem we have another question that we have here so we have our function 32 x square plus 20 x minus 15 we want to know what is x when this function is set equal to 10 so what we do is we'll take that function and set all of that to be equivalent to 10 32 x squared plus 20x minus 15 to track both sides by 10 so you get 0 it was 32 x squared plus 20 x minus 25 now we're we're going to do for this one we want to multiply these two numbers together to get a new number and when we multiply those two numbers together we get 800 very similar to how we did the last problem we want to find all the factors all the numbers that will multiply to 1 to 800 so there's a lot of them and you would kind of go down this list to find a pairing that will hopefully get you to positive 20 as you go through you'll get down to 20 times 40 and you'll get down to 20 and that will become your pairing that you can use to get to 20.
02:18
So now here, instead of going directly and setting the parentheses, we actually need to expand this bad boy first.
02:27
We have 32x squared and then let's expand it by putting 40x minus 20x minus 25.
02:40
So this method is called ac method.
02:43
We multiply our a, which is 32, and our c, which is 25.
02:46
Now we want to group our first two terms and group our last two terms.
02:52
Now the next goal here is fine.
02:54
The numbers are, the terms are similar between our pairings.
02:59
So we look at 32x squared and 40x.
03:01
We see that they both share a 8 and an x.
03:06
So what we're left with on the inside is now 4x and plus 5.
03:12
Now we're going to do the same thing over here and our goal is to end up with 4x plus 5 on the inside.
03:16
So what negative 20x and negative 25 share is they both share a negative 5.
03:24
Pulling out negative 5, i am left with 4x plus 5.
03:30
So cool.
03:31
I ended up with 4x plus 5 in both pairings or groups.
03:36
Now the pieces that i took out, the 8x and the negative 5, become one pair or one factor.
03:45
And then 4x plus 5 becomes the other factor.
03:51
Now, just like the previous problem, we're going to set each one of these equal to zero, excuse me, and solve for x.
03:58
So this first one, we should get that x is equal to five aths.
04:03
And if you're over here, we should get that x is equal to negative five -fourths.
04:11
Now, there's a part b to this question, and now it says using, make sure i'm reading the correct, so use part a to find two points that lie on the graph of the function.
04:24
So we found two x values.
04:29
So now we need to find their corresponding y values.
04:32
So if we do f of 5 aifs first, that will give us 10.
04:40
So we end up with a 0 .5 aves comma 10 is one point on this graph.
04:48
And then we can plug in our other x value, which is negative 5 fourths.
04:53
We plug that in, you also get 10...