Question

Which expression is a prime polynomial? A.x+9y^2 B. 3m+9n C. 8x^7-9x+12x^2 D. x^9-y^6

Answer 1

Answer:

C

Step-by-step explanation:

Answer 2

A prime polynomial is simply an irreducible polynomial.

$\mathbf{x + 9y^2}$ is a prime polynomial

First, we test the options.

$\mathbf{x + 9y^2}$

The above function cannot be reduced further.

Hence, $\mathbf{x + 9y^2}$ is a prime polynomial

$\mathbf{3m + 9n}$

Factor out 3

$\mathbf{3(m + 3n)}$

$\mathbf{3m + 9n}$ is not a prime because it can be factored as $\mathbf{3(m + 3n)}$

$\mathbf{8x^7 - 9x + 12x^2}$

Factor out x

$\mathbf{x(8x^6 - 9 + 12x)}$

$\mathbf{8x^7 - 9x + 12x^2}$ is not a prime because it can be factored as $\mathbf{x(8x^6 - 9 + 12x)}$

Hence, $\mathbf{x + 9y^2}$ is a prime polynomial

Read more about prime polynomials at:

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