Question

which polynomial is prime?

x4 3x2 – x2 – 3
x4 – 3x2 – x2 3
3x2 x – 6x – 2
3x2 x – 6x 3

Answer 1

x^4 + 3x^2 - x^2 - 3 = x^2(x^2 + 3) - 1(x^2 + 3) = (x^2 - 1)(x^2 + 3)
x^4 - 3x^2 - x^2 + 3 = x^2(x^2 - 3) - 1(x^2 - 3) = (x^2 - 3)(x^2 - 1)
3x^2 + x - 6x - 2 = x(3x + 1) - 2(3x + 1) = (x - 2)(3x + 1)
3x^2 + x - 6x + 3 = x(3x + 1) -3(2x - 1); since the content of the two bracket are not the same for this polynomial, that mean it is not factorisable and hence a prime.

Answer 2

The polynomial 3x² + x - 6x + 3  is a prime polynomial

How to determine the prime polynomial?

For a polynomial to be prime, it means that the polynomial cannot be divided into factors

From the list of options, the polynomial (D) is prime, and the proof is as follows:

We have:

3x² + x - 6x + 3

From the graph of the polynomial (see attachment), we can see that the function does not cross the x-axis.

Hence, the polynomial 3x² + x - 6x + 3  is a prime polynomial

Read more about prime polynomial at:

https://brainly.com/question/2944912

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