Factorising...?

Question

I know how to factorise expressions such as:

2x^2+7x-4

into

(2x+4)(x-1)

but how would I factorise x^2-9?

Thanks
Joe

Answer 1

It's the difference of two squares
so
(X+3)(X-3)
the 3x and -3x cancel each other off, which probably threw you off

Answer 2

x^2 - 9 is known as a "difference of squares". It's best to keep your eye out for them, because they are extremely simple to factor. All you have to do is take the square root of each, and then switch signs in the different brackets.

x^2 - 9 = (x-3)(x+3)

What you can also do is look at it this way:

x^2 + 0x - 9

And ask yourself: what two numbers multiply to get -9 but add up to 0? -3 and 3. So you'd factor it like you would factor the problems you're used to.

Answer 3

(x-3)(x+3)

difference of two squares...

a^2-b^2 = (a-b)(a+b)

x^2-9 = (x-3)(x+3)

Answer 4

When you have:
a² - b²

That is:
a² - b² = (a + b)(a - b)

So:
x² - 9 = x² - 3² = (x + 3)(x - 3)

₢

Answer 5

Use the quadratic formula.

http://en.wikipedia.org/wiki/Quadratic_formula