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# Which polynomial is prime?

x⁴ + 3x² - x² - 3

x⁴ - 3x² - x²+ 3

3x² + x - 6x - 2

3x²+ x - 6x + 3

**Solution:**

A prime polynomial has only two factors 1 and itself. It is a polynomial with integer coefficients that cannot be factored into polynomials of lower degrees.

To find the prime polynomial, we will factorize all the polynomials.

**Equation 1: **x^{4} + 3x^{2} - x^{2} - 3 can be factored into (x + 1) (x - 1) (x^{2} + 3). Therefore, it is not a prime polynomial.

**Equation 2: **x^{4} - 3x^{2} - x^{2} + 3 can be factored into (x + 1) (x - 1) (x^{2} - 3). Therefore, it is not a prime polynomial.

**Equation 3:** 3x^{2} + x - 6x - 2 can be factored into (3x + 1) (x - 2). Therefore, it is not a prime polynomial.

**Equation 4:** 3x^{2} + x - 6x + 3 can not be factorized with rational numbers. Therefore, it is a prime polynomial.

## Which polynomial is prime? x⁴ + 3x² - x² - 3, x⁴ - 3x² - x²+ 3, 3x² + x - 6x - 2, 3x²+ x - 6x + 3

**Summary:**

The prime polynomial that cannot be factored into a polynomial of lower degree is 3x^{2} + x - 6x + 3.

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