Question

Which pattern can be used to factor the high-degree polynomial 16x8−49x2 ?(1 point) Responses Neither the difference of squares nor the perfect square trinomial pattern can be used to factor 16x8−49x2. Neither the difference of squares nor the perfect square trinomial pattern can be used to factor 16 x superscript 8 baseline minus 49 x squared . (a−b)2=a2−2ab+b2 left parenthesis a minus b right parenthesis squared equals a squared minus 2 a b plus b squared (a+b)2=a2+2ab+b2 left parenthesis a plus b right parenthesis squared equals a squared plus 2 a b plus b squared (a−b)(a+b)=a2−b2

Answer 1

To factor the polynomial \(16x^8-49x^2\), we can first observe the structure of the polynomial:

1. Notice that it is in the form of a difference of squares. We can rewrite it as:
\[
16x^8 - 49x^2 = (4x^4)^2 - (7x)^2
\]

2. According to the difference of squares pattern, which is given by:
\[
a^2 - b^2 = (a - b)(a + b)
\]
we can assign \(a = 4x^4\) and \(b = 7x\).

3. Applying the difference of squares pattern, we factor:
\[
(4x^4 - 7x)(4x^4 + 7x)
\]

Now, we can see that the polynomial \(16x^8 - 49x^2\) can be factored using the difference of squares pattern. Thus, the correct response is:

**The difference of squares pattern can be used to factor \(16x^8 - 49x^2\).**