Factoring Equations?

Question

Hi,
I'd like ask for an explanation on the method of factoring equations with a number before the first variable. Something like 10x^2 + 15x - 10 for example, were x^2 is preceded by the number 10. Additionally, if it's not too much to ask, I'd like to request an explanation on how to solve 2x-xy^2. Thank you!

Answer 1

In the example you give 10x^2 + 15x - 10, you should first factor out the 5 which is common to all three terms. That leaves 2x^2 +3x -2.
The - before the final term tells you that the factors will be + and -.
You have (2x + )(x-) or the opposite. You know the factors of 2 are 1,2.
So try (2x+2)(x-1) [you know this won't work or you could have factored the 2 out of (2x+2) earlier]
Try (2x+1)(x-2) = 2x^2 -3x -2
Right middle term, but wrong sign.
Therefore reverse the signs.
(2x-1)(x+2) = 2x^2 +3x -2
So the final answer is:
10x^2+15x-10 = 5(2x-1)(x+2)

You solve 2x-xy^2 by first factoring the common factor "x" out of each term.
That leaves x(2-y^2) .
(2-y^2) factors to (sqrt2-y)(sqrt2+y)
so the final answer is
x(sqrt2 - y)(sqrt2 + y)

Answer 2

to simplify, when possible, divide each term by a common factor. Here it is 5. This gives you 2x^2+3x-5. This would then factor (2x+5)(x-1)

Factor out the x. You then have x(2-y^2). This is the best you can do. You are NOT solving anything unless you see an equal sign. You are just factoring.

Answer 3

10x^2 + 15x -10
= 5(2x^2 +3x -2)
=5 (2x -1)(x+2)

2x- xy^2 = x(2-y^2)