polynomials?

Question

x>2 - 3

I need help factoring polynomials. That is just example. Please give me steps so it works everytime.

Answer 1

You have to use different techniques on different types of polynomials.

First you should extract any factor common to every term:
4x^3 - 8x^2 + 12x
= 4x(x^2 - 2x + 3)

Then learn the technique for the difference of two squares:
a^2 - b^2 = (a - b)(a + b)

Progress to simple quadratic expressions with positive coefficients and coefficient 1 for x^2, such as:
x^2 + 5x + 6 = (x + 2)(x + 3)
by considering pairs of numbers which multiply to give 6 and finding the pair which also add to give 5.
When you can do that, you progress to quadratics with negative signs, and then with coefficients other than 1 for x^2.

There are still more techniques master, but that should give you sufficient to start with.

Answer 2

There isn't a guide to factoring, but I can give you some tips.
For quadratic (second degree) polynomials.
1) If there is a common variable in every term, pull it out.
ex. x^3+2x^2+x = x(x^2-2x+1)=x(x-1)(x-1)
2) If there is a perfect square and no first degree term, it is a difference of two squares.
ex. (x^2-1)=(x+1)(x-1)
ex. (x^2-81)=(x+9)(x-9)

3) If you have a quadratic and the signs are both positive, you'll have two plus signs in your factors.
If you have two negative signs, you'll have a positive and a negative sign in your factors.
If you have one positive and one negative sign, you'll have one positive and one negative.

Answer 3

That's not a polynomial.

If what you mean is x^2 - 3, then it can be factored as:
(x - rad3)(x + rad3)