How do you find factored form?

Question

Is there any freaking rule or formula that can be used or applied to the certain types? I hate this so much and I want to cry my freaking head off, I don't under-freaking-stand it at all. Thanks.

Answer 1

Factoring can be done in so many ways. Here are some of the most common examples:

--------------------------

(1) xy + x

Factors into

x (y + 1)

All you basically do with that is remove the like term from each, pull it out as one factor, and what is left is the second factor.

Another example:

5x + 15xy + 20xz

Becomes:

5x ( 1 + 3y + 4z)

------------------------

(2) x² - y²

This is called the difference of two squares. The rule for factoring these is:

(x - y)(x + y)

----------------------------

(3) x³ + y³

The sum of two cubes factors:

(x + y)(x² - xy + y²)

-------------------------------

(4) x³ - y³

The difference of two cubes factors:

(x - y)(x² +xy + y²)


Hope that helps a little.

Answer 2

There is no quick and fast rule on how to approach a given factoring problem. That makes factoring a real pain to learn. You just have to pick up a few different techniques and then practice a lot - there's no way around that.

I'll presume you're dealing with factoring an equation of form ax^2 + bx + c into form (gx+h)*(jx+k).

Here's an example of how I do that. Suppose I'm trying to factor x^2 +x - 6.

I always start by looking at the last term. In this example, that's the -6 at the end. That -6 can be the product of either -6*1, 6*-1, -3*2, or 3*-2.

This tells me that we're dealing with either (x-6)(x+1), (x+6)(x-1), (x-3)(x+2), or (x+3)(x-2).

Next, I look at the middle term of the equation I'm factoring: in this case, +x. That term tells me which of the four candidates is correct. In this case, it's (x+3)(x-2).

If you don't see why that's the correct candidate, get some practice. multiply out all four of the candidates, and you should start seeing a pattern.

Hopefully that helps. I know it's tricky; factoring is a tricky thing to explain too.

Answer 3

First off: Make sure you understand how to multiply binomials, trinomials, etc. If you're weak in that, you'll *never* understand what factoring is all about.

Second: There are 'example problems' in your book. Set down and *work* them, right along step-by-step with the book.

Third: Just practice your αss off ☺

Symbolic manipulation is probably not the easiest thing in the World to learn (and I doubt it's in 2'nd or 3'rd place, either ☺) but it is one of the most powerful tools ever invented by the human mind.


Doug

Answer 4

you can use the following formulas
1.difference of two squares
(a^2-b^2)=(a+b)(a-b)
2.(a^2+2ab+b^2)=(a+b)(a+b)
=>(a+b)^2
3.(a^2-2ab+b^2)=(a-b)(a-b)
=>(a-b)^2
4a^3+b^3=(a+b)(a^2-ab+b^2)
5.a^3-b^3=(a-b)(a^2+ab+b^2)
6.a^3+b^3+c^3-3abc=
(a^2+b^2+c^2-ab-bc-ca)
7.a^3+3a^2b+3ab^2+b^3=>
a^3+3ab(a+b)+b^3=(a+b)^3
8.a^3-3ab(a-b)-b^3=(a-b)^3
9.a^2+b^2+c^2+2ab+2bc+2ca
=(a+b+c)^2