# Which polynomial is prime x 3 3x 2 2x 6

Asked by wiki @ in **Mathematics** viewed by 309 People

Which polynomial is prime?

x3 + 3x2 + 2x + 6

x3 + 3x2 – 2x – 6

10x2 – 4x + 3x + 6

10x2 – 10x + 6x – 6

Asked by wiki @ in **Mathematics** viewed by 309 People

Which polynomial is prime?

x3 + 3x2 + 2x + 6

x3 + 3x2 – 2x – 6

10x2 – 4x + 3x + 6

10x2 – 10x + 6x – 6

Answered by wiki @

we know that

If the only factors a polynomial are and itself, then that polynomial is prime.

so

If the polynomial has at least one root (one x-intercept) then the polynomial is not prime

Using a graph tool

__case 1) __

see the attached figure N 1

The polynomial has one root-------> the polynomial is not prime

__case 2) __

see the attached figure N 2

The polynomial has three roots-------> the polynomial is not prime

__case 3) __

see the attached figure N 3

The polynomial has zero roots-------> the polynomial is prime

__case 4)__

see the attached figure N 4

The polynomial has two roots-------> the polynomial is not prime

therefore

__the answer is__

** ------> is prime**

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