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

Answered by wiki @



we know that

If the only factors a polynomial are  1 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)

 x^{3}+ 3x^{2} + 2x+ 6

see the attached figure N 1

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

case 2)

 x^{3} + 3x^{2} - 2x - 6

see the attached figure N 2

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

case 3)

 10x^{2}-4x+3x + 6

 10x^{2} -x + 6

see the attached figure N 3

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

case 4)

 10x^{2}-10x+6x - 6

 10x^{2} -4x - 6

see the attached figure N 4

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

therefore

the answer is

 10x^{2}-4x+3x + 6 ------> is prime


Do you know the better answer?

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