To factor the polynomial [tex]\( 4x^2 - 16 \)[/tex], follow these steps:
1. Identify the common factor: Notice that each term in the polynomial [tex]\( 4x^2 - 16 \)[/tex] has a common factor of 4.
[tex]\[
4x^2 - 16 = 4(x^2 - 4)
\][/tex]
2. Factor the quadratic expression [tex]\( x^2 - 4 \)[/tex]: Recognize that [tex]\( x^2 - 4 \)[/tex] is a difference of squares. This can be factored using the formula [tex]\( a^2 - b^2 = (a - b)(a + b) \)[/tex].
Here, [tex]\( a = x \)[/tex] and [tex]\( b = 2 \)[/tex]. Consequently,
[tex]\[
x^2 - 4 = (x - 2)(x + 2)
\][/tex]
3. Combine the factored forms: Substitute the factored form of [tex]\( x^2 - 4 \)[/tex] back into the expression with the common factor 4.
[tex]\[
4(x^2 - 4) = 4(x - 2)(x + 2)
\][/tex]
Therefore, the factored form of the polynomial [tex]\( 4x^2 - 16 \)[/tex] is [tex]\( 4(x - 2)(x + 2) \)[/tex].
Hence, the correct answer is:
C. [tex]\( 4(x+2)(x-2) \)[/tex]
