Question

Use the polynomial identity x2−a2=(x+a)(x−a) to rewrite x2−196 . Which polynomial does this establish?(1 point) Responses x2 −196=(x−98)(x+98) x2 −196=(x−98)(x+98) 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−14)(x−14)

Answer 1

To rewrite \( x^2 - 196 \) using the polynomial identity \( x^2 - a^2 = (x + a)(x - a) \), we need to identify \( a \). Here, we have:

\[ a^2 = 196 \]

Taking the square root of both sides, we get:

\[ a = 14 \]

Now we can apply the identity:

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

So the correct rewriting of \( x^2 - 196 \) is:

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

Among the provided responses, the correct one is:

\( x^2 - 196 = (x + 14)(x - 14) \) (this response is listed twice).

Therefore, you can choose either of the options that display \( x^2 - 196 = (x + 14)(x - 14) \).

Answer 2

x^2 - 196 = (x + 14)(x - 14) \), no there not both the same one of them is x^2 +++++ 196 = (x + 14)(x - 14) \)

Answer 3

I apologize for the confusion in interpreting your previous message. However, let's clarify things.

The correct factorization using the identity \( x^2 - a^2 = (x + a)(x - a) \) is indeed:

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

There was no expression of the form \( x^2 + 196 \) in your initial question, which is why it should strictly remain as \( x^2 - 196 \).

Summarizing the correct factorization:

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

If any of the responses indicated a polynomial of the form \( x^2 + 196 \), then that would be incorrect in this context since it does not relate to the original expression \( x^2 - 196 \).

Again, the factorization we are confirming is:

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

Please ensure you choose the option that correctly states this factorization. If there were multiple similar responses, they need to be distinctly articulated to avoid confusion. Thank you for your understanding!