We want to state which special factoring pattern, if any, the given polynomial function follows.
x2−4
Note that the exponent of x is 2, and that 4 can be written as 22. Moreover, we have subtraction separating the terms. Therefore, the given expression follows the pattern difference of two squares.
x2−22
We want to state which special factoring pattern, if any, the given polynomial function follows. 3x3+5 Neither 3x3 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.
We want to state which special factoring pattern, if any, the given polynomial function follows. 4x2+25 Note that the first term can be written as (2x)2, and that 25 can be written as 52. 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.
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 33, and that 1000 can be written as 103. 27x3+1000⇔(3x)3+103 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+103
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. 64x3−x2+1 Furthermore, note that, although 64 is a perfect square, 64x3 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.