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We want to state which special factoring pattern, if any, the given polynomial function follows.
$x_{2}−4 $
Note that the exponent of $x$ is $2,$ and that $4$ can be written as $2_{2}.$ Moreover, we have subtraction separating the terms. Therefore, the given expression follows the pattern $difference$ of two $squares.$

$x_{2}−2_{2} $

b

We want to state which special factoring pattern, if any, the given polynomial function follows. $3x_{3}+5 $ Neither $3x_{3}$ nor $5$ can be written as perfect squares or cubes. Therefore, the given expression is not a difference of two squares, a sum of two cubes, or a difference of two cubes. We also see the expression has only two terms. This means it is not a perfect square trinomial. Consequently, it does not follow any special factoring pattern.

c

We want to state which special factoring pattern, if any, the given polynomial function follows. $4x_{2}+25 $ Note that the first term can be written as $(2x)_{2},$ and that $25$ can be written as $5_{2}.$ However, there is addition separating the terms. Therefore, the given expression is not a difference of two squares, a sum of two cubes, or a difference of two cubes. Moreover, the expression is not a perfect square trinomial because it only has two terms. Consequently, it does not follow any special factoring pattern.

d

We want to state which special factoring pattern, if any, the given polynomial function follows. Note that the exponent of $x$ is $3,$ that $27$ can be written as $3_{3},$ and that $1000$ can be written as $10_{3}.$ $27x_{3}+1000⇔(3x)_{3}+10_{3} $ We can see that both terms of the expression are perfect cubes. Moreover, the terms are separated by addition. Therefore, the given expression follows the pattern $sum$ of two $cubes.$ $(3x)_{3}+10_{3} $

e

We want to state which special factoring pattern, if any, the given polynomial function follows. Since it has three terms, we know it is not a difference of two squares, a sum of two cubes, or a difference of two cubes. $64x_{3}−x_{2}+1 $ Furthermore, note that, although $64$ is a perfect square, $64x_{3}$ is not perfect square because the exponent of the $x-$variable is $3.$ This means, the expression is not a perfect square trinomial. Therefore, it does not follow any special factoring pattern.