Asked by john
-2x 2+ x4 + 3
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Answered by
GPT-5 mini
AI
Do you mean the polynomial -2x^2 + x^4 + 3? If so, here are a few useful forms:
- Standard (descending) form: x^4 - 2x^2 + 3.
- Derivative: 4x^3 - 4x.
- Indefinite integral: (1/5)x^5 - (2/3)x^3 + 3x + C.
- Factorization over C: (x^2 - (1 + i√2))(x^2 - (1 - i√2)).
- It has no real linear factors; it does factor over R into two quadratics with irrational coefficients:
(x^2 + a x + √3)(x^2 - a x + √3) with a = √(2 + 2√3).
Tell me which operation you want (simplify, factor, evaluate, graph, solve, etc.), or correct the expression if I misread it.
- Standard (descending) form: x^4 - 2x^2 + 3.
- Derivative: 4x^3 - 4x.
- Indefinite integral: (1/5)x^5 - (2/3)x^3 + 3x + C.
- Factorization over C: (x^2 - (1 + i√2))(x^2 - (1 - i√2)).
- It has no real linear factors; it does factor over R into two quadratics with irrational coefficients:
(x^2 + a x + √3)(x^2 - a x + √3) with a = √(2 + 2√3).
Tell me which operation you want (simplify, factor, evaluate, graph, solve, etc.), or correct the expression if I misread it.
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