Can I use a factoring company to buy a profitable business ?
You are talking about buying a business based upon its receiveables. Borrowing against the receivables to finance the business. I highly doubt it. Keep in mind factoring is going to be like getting 70% of the value of the invoice.It might be possible, call a factoring company, be prepared to have a resume that shows why you can run this company.
What are some techniques for factoring polynomials of degree higher than 2?
There are three main ways to factor equations with degree higher than 2:
1. For cubics there are rules for factoring the sum or difference of cubes. Memorize them.
2. For relatively small degrees above 2, grouping can sometimes be used.
3. The most general method is to look at the graph or use the rational roots theorem to find at least one root, convert the root(s) just found into factor(s) using the factor theorem, then divide the original function by those factor(s). Then perhaps apply the method again to the reduced function.
when you have a difference of squares (x^2 - y^2) this is equal to (x+y)(x-y)
1. 100x^2 - 64y^2 = (10x+8y)(10x-8y)
another technique is expanding and grouping
in the equation y=ax^2 + by + c, you multiply a and c together. Then you find factors of ac that add up to b
2. n^2 - 5n - 36
factors that add up to -5 are -9 and 4
therefore, you can also say
n^2 - 9n + 4n - 36
this does not effect the value, so we are okay. Now you group this by working with the first two and last two terms separately.
n^2 - 9n = n(n-9)
4n - 36 = 4(n-9)
therefore, the whole thing is
n(n-9) + 4(n-9)
the fact that (n-9) shows up there twice , which means we are okay
now we can distribute out the (n-9)
when it is possible to distribute out a factor initially, go ahead and do so.
3. 2a^3 + 16a^2 + 30a
2a(a^2 + 8a + 15)
all of a sudden, this is so much easier to factor. Facotrs of 15 that add up to 8 are 5 and 3
you end up with
4. 6x^2 + 20x - 16
2 (3x^2 + 10x - 8)
2 (3x^2 -2x + 12x - 8)
3 [x(3x-2) + 4(3x-2)]
5. 9x^2 + 12x + 4
9x^2 + 6x + 6x + 4
3x(3x+2) + 2(3x+2)
I did this work, but by looking at the first and last terms, you know they are both perfect squares, so there was a pretty good chance that the whole polynomial was a squared binomial....it's a bit complicated, so just use the expansion and grouping method.
Here is a great tool to help you step by step through any factoring problem you have (you can plug in any problem and it will show you how it's done. It's like a calculator that can factor)
To understand factoring, it helps to understand multiplying polynomials. If you multiply (x) (x+2), you will get (x^2+2x). Make sure you understand this: x times x gives you the result x squared. 2 times x gives you 2 x. You should also understand that one of the properties of multiplication is that multiplication is distributive over addition. Take the time to understand this: if you have a problem (6) (3+1), you can rewrite it and rework it as (6 times 3) +(6 times 1). (6) (4) = 24 and (18) + (6) = 24. Know this and feel comfortable with it because factoring is just the reverse of this - you're just undoing this operation.
Practice it - there are text books with tons of examples.
The problem you gave to factor is: y^2+5y-6.
You know that the first term (terms are separated by plus or minus signs) is y^2.
What times y gives you y squared? y itself.
So you know you are going to have a least two factors - start building the factors now. The first term of each is going to be y. That's because you are going to multiply the first terms together and they are going to give you y^2.
Now look at the last term in your problem expression: it is -6.
It is also going to be the result of multiplying two things together so make a list of all the things that when multiplied together, give you -6.
Since -6 can only be produced by multiplying a negative and a positive to produce a negative, keep that in mind while you make your list.
The list of possibilities:
That pretty much exhausts the list of numbers that multiplied together produce -6. Look at the list: which pair, WHEN ADDED TOGETHER, give you the middle term of your problem expression? 6 and -1. Only one pair is going to work and that one is it. 6-1=5 and your middle term is 5y.
So now modify what you have been building (which are factors of your expression).
These are your factors. You are done factoring. It's done.
You have to be able to multiply these two factors out to get your original problem expression and you should always do it to make sure they are correct. The FOIL method is usually used. F is first terms, O is outer terms, I is inner terms, L is last terms. You systematically multiply terms (given that order; it's just a memory trick to guide you through..). After you multiply your terms out, you add them up and it gives you your original problem expression.
F (first) y * y = Y^2
O (outer) y * -1 = -1y
I (inner) 6 * y = 6y
L (last) 6 * -1 =-6
Add the products together Y^2 -1y +6y -6
Add the 6y and -1y and you get 5y.
Put this in descending order from the highest power and you get y^2+5y-6. That's your original expression and you factored it.
Sounds like a lot of work but if it's not really. If you sit down and work 25 of these problems, you will feel more comfortable with it. After you've worked 50, you will be able to do them (create 2 factors from one expression) in your head.