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 the expression \( x^2 - 196 \) using the polynomial identity \( x^2 - a^2 = (x + a)(x - a) \), we can identify \( a^2 \) with \( 196 \).

Since \( 196 = 14^2 \), we can set \( a = 14 \). Now we can apply the identity:

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

Thus, the expression \( x^2 - 196 \) can be rewritten as:

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

This establishes the polynomial \( (x + 14)(x - 14) \).