Use the polynomial identity x2−a2=(x + a)(x − a)

Question

to rewrite x2−196
. Which polynomial does this establish?(1 point)
Responses

x2−196 = (x − 14)(x − 14)
x2−196 = (x − 14)(x − 14)

x2−196 = (x + 98)(x − 98)
x2−196 = (x + 98)(x − 98)

x2−196 = (x − 98)(x − 98)
x2−196 = (x − 98)(x − 98)

x2−196 = (x +14)(x − 14)

Answer 1

To rewrite \(x^2 - 196\) using the polynomial identity \(x^2 - a^2 = (x + a)(x - a)\), we first identify \(a\).

Since \(196 = 14^2\), we have \(a = 14\).

Now we can apply the identity:

\[ x^2 - 196 = x^2 - 14^2 = (x + 14)(x - 14) \]

Therefore, the correct response is:

\(x^2 - 196 = (x + 14)(x - 14)\).