Respuesta :

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

I only see the polynomial [tex] x^2-36 [/tex], 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 [tex] x_i [/tex] we write the factor [tex] (x-x_i) [/tex], and decompose the polynomials like this:

[tex] x^2-36=0 \iff x^2 = 36 \iff x = \pm\sqrt{36} = \pm 6 [/tex]

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

[tex] x^2-36 = (x+6)(x-6) [/tex]

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

[tex] a^2-b^2 = (a-b)(a+b) [/tex]

which again leads to

[tex] x^2-36 = (x)^2 - (6)^2 = (x+6)(x-6) [/tex]