Learn Which Polynomial Is Prime X4 3x2 X2 3
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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:  x4 + 3x2 - x2 - 3 can be factored into (x + 1) (x - 1) (x2 + 3). Therefore, it is not a prime polynomial.

Equation 2: x4 - 3x2 - x2 + 3 can be factored into (x + 1) (x - 1) (x2 - 3). Therefore, it is not a prime polynomial.

Equation 3: 3x2 + x - 6x - 2 can be factored into (3x + 1) (x - 2). Therefore, it is not a prime polynomial.

Equation 4: 3x2 + 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 3x2 + x - 6x + 3.

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