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Answer :
Final answer:
To factor the expression 5x⁷+15x⁶−20x⁵−60x⁴, start by factoring out the greatest common factor, then factor the trinomial inside the parentheses, and finally further factor using the difference of squares formula.
Explanation:
To factor the expression 5x⁷+15x⁶−20x⁵−60x⁴, we start by factoring out the greatest common factor, which in this case is 5x⁴. Factoring out 5x⁴ from each term, we get:
5x⁴(x³ + 3x² - 4x - 12)
Next, we can factor the trinomial inside the parentheses. We can use grouping or any other factoring method. One way to factor the trinomial is:
5x⁴(x²(x + 3) - 4(x + 3))
Now, we can notice that (x + 3) is a common factor in both terms. Factoring it out, we get:
5x⁴(x + 3)(x² - 4)
Finally, we can further factor the expression x² - 4 using the difference of squares formula. It becomes:
5x⁴(x + 3)(x + 2)(x - 2)
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