Question

Why is x² + 36 NOT factorable? In other words, why is it prime? What are twodetails that draw you to this conclusion?

Answer 1

Step 1:

In this question, we are given the following:

a) Why is x² + 36 NOT factorable?

b) In other words, why is it prime?

c) What are two details that draw you to this conclusion?

Step 2:

The details of the solution are as follows:

`\begin{gathered} a)\text{ x}^2\text{ + 36 is not factorizable under of field of integers Z,} \\ since\text{ it cannot be expressed as product of two squares} \end{gathered}`

b) In other words, why is it prime?

It is a prime polynomial because a prime polynomial is one that cannot be factored into the product of two polynomials, using integer values.

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c) What are two details that draw you to this conclusion?

1) You can factor a difference of squares, but not a sum of squares.

2) A prime polynomial is one that cannot be factored into the product of two polynomials, using integer values.

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