Algebra-2

According to the Rational Root Theorem, for a polynomial equation , the possible rational roots are of the form , where  is a factor of the constant term  and  is a factor of the leading coefficient .

 

For the equation , the leading coefficient is 2 and the constant term is -12.

 

Factors of -12 are ±1, ±2, ±3, ±4, ±6, ±12.

Factors of 2 are ±1, ±2.

 

So the possible rational roots are ±1/1, ±1/2, ±2/1, ±2/2 (which simplifies to ±1), ±3/1, ±3/2, ±4/1, ±4/2 (which simplifies to ±2), ±6/1, ±6/2 (which simplifies to ±3), ±12/1, ±12/2 (which simplifies to ±6).

 

Now we test these possible roots one by one.

 

Testing :

Substitute  into the equation: .

 

Testing :

Substitute  into the equation: .

 

Testing :

Substitute  into the equation: