Use the polynomial identity x2−a2=(x+a)(x−a) to rewrite x2−196 . Which polynomial does this establish?(1 point)Responsesx2−196=(x+98)(x−98)x squared minus 196 equals left parenthesis x plus 98 right parenthesis left parenthesis x minus 98 right parenthesisx2−196=(x−14)(x−14)x squared minus 196 equals left parenthesis x minus 14 right parenthesis left parenthesis x minus 14 right parenthesisx2−196=(x−98)(x−98)x squared minus 196 equals left parenthesis x minus 98 right parenthesis left parenthesis x minus 98 right parenthesisx2−196=(x+14)(x−14)

Question

Use the polynomial identity  x2−a2=(x+a)(x−a)  to rewrite  x2−196 . Which polynomial does this establish?(1 point)Responsesx2−196=(x+98)(x−98)x squared minus 196 equals left parenthesis x plus 98 right parenthesis left parenthesis x minus 98 right parenthesisx2−196=(x−14)(x−14)x squared minus 196 equals left parenthesis x minus 14 right parenthesis left parenthesis x minus 14 right parenthesisx2−196=(x−98)(x−98)x squared minus 196 equals left parenthesis x minus 98 right parenthesis left parenthesis x minus 98 right parenthesisx2−196=(x+14)(x−14)

GPT-4o mini · Answer

To rewrite $ x^2 - 196 $ using the polynomial identity $ x^2 - a^2 = (x + a)(x - a) $, we identify $ a^2 $ with 196. This means $ a = 14 $ since $ 14^2 = 196 $. Thus, we can rewrite $ x^2 - 196 $ as: $$ x^2 - 196 = x^2 - 14^2 = (x + 14)(x - 14) $$ So the polynomial identity we established is: $$ x^2 - 196 = (x + 14)(x - 14) $$ Looking through the responses, the correct one is: **$ x^2 - 196 = (x + 14)(x - 14) $**.