Answer :
Final answer:
The polynomial -3x⁴ - 9x³ + 15x² can be factored by first finding the common factor, which is -3x², resulting in -3x²(x² + 3x - 5). This is the most simplified form.
Explanation:
To factor the polynomial -3x⁴ - 9x³ + 15x², we first look for a common factor in the coefficients of the terms. In this case, the common factor is -3x². So, we can factor -3x² out of each term. Our polynomial becomes:
-3x²(x² + 3x - 5).
This leaves us with a problem of factoring a quadratic equation in the form ax² + bx + c = 0. However, the quadratic x² + 3x -5 cannot be further factored using integer coefficients, so the complete factorization of the original polynomial is -3x²(x² + 3x - 5).
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