how do you factor polynomials that look like this: x^2 - 4?

Question

that is, x squared ... and then minus 4. not x^(2-4)

Answer 1

difference of squares rule:

x^2 - y^2

(x-y)(x+y)

Answer 2

That's called the difference of two squares. Whenever any polynomial like that is just an X squares term and a constant that can be perfectly square rooted with a minus sign in between you'll always factor it by taking the square root of both terms and writing it like so:

(x+2)(x-2)

works for all polynomials that are differences of two squares

Answer 3

This is an expression which is the difference of two squares. Take the sqrt of both terms and factor into two brackets, one consisting of their sum and one of their difference:

(x+2)(x-2)

Another example would be, say 9x^2 - 16, which would factor as:

(3x+4)(3x-4)

You can check this works by multiplying them back out!

Answer 4

(x^2-4) = (x-2)(x+2)

Answer 5

(x+2)(x-2)

Answer 6

x^2 - 4 can be factored:

(x-2)(x+2)

if you check it by multiplying terms then:

x^2 - 2x +2x - 4
collecting x^2-4

Answer 7

x^2 - 4 =(x-2)(x+2)
more generally, if you have
x^2 -b^2 =(x-b) (x+b)
]

Answer 8

x^2 + 5x - 24 x^2 + 8x - 3x - 24 x ( x+ 8 ) - 3( x+ 8) (x + 8) (x - 3)

Answer 9

x^2z-y^2z always equals (x^z-y^z) therefore x^2-4 = (x+2)(x-2)