Identify if the given polynomial is a polynomial with common monomial factor (CMN), difference of two squares (DTS), perfect square trinomial (PST), or sum or difference of two cubes (SDC). Then, factor each completely.
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Answer:
1. CMF
8xy + 10xz - 14xw = 2x(4y + 5z - 7w)
2. PST
-2x² + 12x + 40 = -2(x² - 6x - 20)
3. CMF
4xy - 6xz + 12xw = 2x(2y - 3z + 6w)
4. PST
x² - 22x + 121 = (x - 11)(x - 11)
5. PST
36x² - 12x + 1 = (6x - 1)(6x - 1)
6. DTS
1 - 9x² = (1 - 3x)(1 + 3x)
7. DTS
x²y⁴ - 25 = (xy² + 5)(xy² - 5)
8. SDC
x³ - 125 = (x - 5)(x² + 5x + 25)
9. SDC
27x³ + 8y³ = (3x + 2y)(9x² - 6xy + 4y²)
10. SDC
1000x³ - 1 = (10x - 1)(100x² + 10x + 1)