Use the polynomial identity x^2-a^2=(x+a)(x-a) to rewrite x^2-196. Which polynomial does this establish?

Answer 1

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

Here, we can see that \( 196 \) can be expressed as \( 14^2 \) because \( 14 \times 14 = 196 \). Thus, we have:

\[ a^2 = 196 \implies a = 14. \]

Now, we can apply the polynomial identity:

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

Therefore, the polynomial \( x^2 - 196 \) can be rewritten as:

\[ (x + 14)(x - 14). \]