Question

Factor each polynomial x2-36

Answer 1

I only see the polynomial
`x^2-36`, so I'll factor that one.

We can use two approaches: the most "standard" one requires us to find the roots of the polynomial. Then, for each root
`x_i` we write the factor
`(x-x_i)`, and decompose the polynomials like this:

`x^2-36=0 \iff x^2 = 36 \iff x = \pm√(36) = \pm 6`

So, the root
`6` yields the factor
`(x-6)`, and the root
`-6` yields the factor
`(x+6)`. This means that the polynomial can be factored as

`x^2-36 = (x+6)(x-6)`

Alternatively, you can observe that the polynomial comes in the form
`a^2-b^2`, and it can be factored as

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

which again leads to

`x^2-36 = (x)^2 - (6)^2 = (x+6)(x-6)`

Answer 2

(x+6)(x-6) would be the factored form