# Which polynomial is prime?

x³ + 3x² - 2x - 6

x³ - 2x² + 3x - 6

4x⁴ + 4x³ - 2x - 2

2x⁴ + x3 - x + 2

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

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

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

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

## Which polynomial is prime? x³ + 3x² - 2x - 6, x³ - 2x² + 3x - 6, 4x⁴ + 4x³ - 2x - 2, 2x⁴ + x3 - x + 2

**Summary:**

The prime polynomial that cannot be factored into a polynomial of lower degree is 2x^{4} + x^{3} - x + 2.