Which polynomial is prime? 
x² + 9, x² - 25, 3x² - 27, 2x² - 8 

Solution:

We know that a prime polynomial cannot be reduced

Let us consider all the options

1) x² + 9 cannot be reduced.

2) x² - 25

Using the algebraic identity (a² - b²) = (a + b)(a - b)

x² - 25 = (x + 5) (x - 5)

3) 3x² - 27

= 3(x² - 9)

Using the algebraic identity (a² - b²) = (a + b)(a - b)

= 3(x + 3)(x - 3)

4) 2x² - 8

= 2(x² - 4)

Using the algebraic identity (a² - b²) = (a + b)(a - b)

= 2(x + 2)(x - 2)

Therefore, x² + 9 is prime.

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Which polynomial is prime?
x² + 9, x² - 25, 3x² - 27, 2x² - 8

Summary:

x² + 9 is the polynomial which is prime. We know that a prime polynomial cannot be reduced