Can anyone help explain factoring to me?

Question

I've been a little lost in class because I really don't know how to factor :\ Can anyone help me out?

well, there's not a particular problem that i can give you. i'm not doing homework or anything. Hmm. okay, without doing the quadratic formula, how can you factor this? x^2+3x-4. they say the answer is (x+4)(x-1)=0, but i don't know how get that. help?

Answer 1

Just read this thoroughly, and I promise you'll understand:

For your problem:
x^2+3x-4. they say the answer is (x+4)(x-1)=0.

Look at your the equation you have. First thing you want to do is draw parentheses, like so.: ( )( )

This way, you already know where to fill stuff in. Now, you want to look at your equation's + and - signs. Look at the second sign; it's a - . This tell you that the signs in two set of parentheses will be DIFFERENT. So, draw one parentheses with a plus sign, and one with a minus sign.

( + )( - )

Now look at your equation again. x^2 + 3x - 4.
Well, you know that x times x = x^2. And you know that x^2 is the first term in that equation. Since x times x is the only multiplication that will equal x^2, you're going to put an x in the first spot in each parentheses. Like this:

(x + __) (x - __)

Now look at the last term in your equation. It's a 4. What numbers can you mulitply together to get 4? Well, either:
1 X 4 or 2 X 2. right? Look at the middle term 3x. Which of those two sets of numbers can you either add or subtract to make 3?

1 and 4, right? So, now you know that 1 and 4 are going to be going into your parentheses. But, which ones do they go in? The first or the second?

Go back to your equation and look at the first sign. It's a + sign. This means that the parentheses with the bigger second number will be POSITIVE. So you know the 4 will be going in the parentheses with the + sign. Which gives you:

( x + 4)(x - 1)

Ta-da!

Answer 2

x^2 + 3x -4 is the example you gave to factor this look at the first term and determine two number multiplie dtogether that will equal that term. obviously this is x and x this is the first term of each factor:

(x )(x )

now you need 2 numbers that when multiplie together give the third term but when added they give the second term.
obviously one has to be minus because the last term is negative. and the larger of the two numbers must be positive because when they are added together the result must be the +3 in the second term. two numbers multiplied together to get -4 could be -1 and 4. thry these: if they dont work then reverse the negative signs.

( x - 1)(x + 4)

the first two numbers multiplied together are x^2
then 4x -1x = 3x
and -1(4) =-4

the above three numbers are the original expression so the factors are correct. As you can see factoring can amount to a lot of trial and error.

Answer 3

there are 3 types of factoring.
GCF, difference of perfect squares and trinomial.

GCF means greatest common factor, the biggest number that all the other numbers can divide by. for example, if u have to factor 2x^2+2X+ 2 you can take out a 2 and u get .....
........................2(x^2 + x +1)

difference of prefect sqaures means that one perfect square is being subtracted from another. a perfect squarre has a rational square root (sqrt). for example, 4 is a perfect square since its sqrt is 2. If u have to factor x^2 - 4 you write.... (x+2) (x-2). notice that i wrote the same thing twice except for the sign in between.

the hardest one is trinomial. you have to find 2 numbers that add up the middle term and multiply to be the final term. for example, if u have to factor x^2-2x+1 u say that -1 and -1 add up to be -2 and multiply to be +1. therefore u write (x-1) (x-1).

if they tell u to factor completely, u might have to use a combination of different methods i showed u.

Answer 4

Factoring is finding all the combinations that multiply to number you are trying to factor. For basic numbers it is simply a trial and error thing based on your multiplication tables. In algebra it becomes a little more diversified and I forget the methods since I graduated 40 years ago. maybe others will provide better help.

Answer 5

Factoring means breaking something into its smallest constituents. So, if your finding the prime factorization of a number, you're finding the prime numbers that will multiply out to that number. As for factoring an equation, you're breaking it down into the product of simpler equations, until you can't break it down anymore.

Answer 6

each little thing which you get carry of by your 5 senses effects you ideas, and subsequently you psychological wellbeing. surroundings is thought to be the foremost element, and has a great impact on the way one perceives certainty. It of direction plenty greater complicated than this simplistic rationalization. you may desire to evaluate psychology to start to understand the human ideas.

Answer 7

factorising is sort of to take out what is common in an equation

for example factorise this : x^2 -3x+5x^3

take out the common x to get

x(x-3+5x^2)

Answer 8

http://library.thinkquest.org/20991/alg/factoring.html
http://www.purplemath.com/modules/factquad.htm
http://www.algebrahelp.com/calculators/expression/factoring/

Answer 9

sure. but what's your problem?