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Answer :
Final answer:
The expression ˣ⁴ + 6ˣ³ - 27ˣ² - x² - 6x + 27 can be factored by grouping, with the result being (ˣ³ - ˣ² + 9)(ˣ + 6).
Explanation:
The expression from the question is ˣ⁴ + 6ˣ³ - 27ˣ² - x² - 6x + 27. To factor this expression, we first arrange the terms in pairs. The terms ˣ⁴, 6ˣ³ share a common factor of 'ˣ³', while -27ˣ², -x² share a common factor of '-ˣ²', and -6x, 27 share a common factor of '3'.
Therefore, the expression can be re-written as: ˣ³(ˣ + 6) - ˣ²(27 - 1) + 3(-2x + 9). Now, if we look closely, we can see that (ˣ + 6) appears in both the first and second term. Furthermore, we can break down the third term as 3 * 3(3 - 2x). Now the expression becomes: ˣ³(ˣ + 6) - ˣ²(ˣ + 6) + 9(3 - 2x).
Therefore, the factored form of the given expression is (ˣ³ - ˣ² + 9)(ˣ + 6)
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