need algebra help please :/

[keybladeninja11]

just a few things here...

1) Find two consecutive natural numbers whose product is 182. (Use an algebraic equation to solve this.)

...first of all, what exactly are consecutive natural numbers? i cant figure this question out so it would really help if someone could please give me a step-by-step on how to solve this

2) Solve the quadratic equation by factoring.
x^2 = 24-2x

3) What is the domain of the following?
g(x) = (x-1)/(3x-2)

(and really, i have trouble finding the domain of any of kinds of equations so if you can give me a general of how to find domain, it would be really helpful)

and last 4) Find all real values such that f(x) = 0 where f(x) = (3/(x-1)) + (4/(x-2)) (Do not substitute 0 for x)

it would really help if i could solve these, thank you!

[Incompris]

Here's the first two.

1) Natural numbers are the numbers you use while counting (i.e. 1, 2, 3, 4.... 67, 68, 69, etc)

Consecutive means they come right after each other, for example 1 and 2 are consecutive because 2 follows 1 directly.

You need to assign a variable to both numbers in the problem. It says two consecutive natural numbers, so the bigger number would be 1 more than the smaller one. Here is your variables:

X = smaller number
X + 1 = second number

"product" means the result of multiplying the two numbers together. So the product of X and X + 1 is 182.

Here is your equation:
x (x+1) = 182

Can you solve it from there?

Once you get what X equals, you will need to go back and find the second number, so plug it into your X + 1 equation and you will have your two consecutive natural numbers. (I know that part is a no brainer but it's good to show your work anyway so in the future when you have much harder questions you know how to do it.)

2)
Factor it out.

So you start with

x^2 = 24-2x

take the right numbers over to the left, so it equals 0. (sorry for the dots, the site wouldn't let me space it out)

x^2 ........... = 24 - 2x
.......+2x -24... -24 +2x

x^2 + 2x - 24 = 0

Factoring can be tricky. But here's how it works. We are going back to the form (x + a)(x + b) from where we are now. To do that we need to figure out what a and b were.

First multiply the number that comes before the x^2 and the number without a variable. Because the x^2 doesn't have a number in front of it, it is a 1, so (1)(-24) = -24

Next you need to find two numbers when multiplied together equals -24(from our previous step) and when added together equals 2 (the number that is attached to the x) The answer to this is 6 and -4.

So the answer is (X + 6)(X - 4)

[keybladeninja11]

you really helped, thanks a lot!