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 -6.

Factors of -6 are ±1, ±2, ±3, ±6.

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, ±6/1, ±6/2 (which simplifies to ±3).

Now we test these possible roots one by one.

Testing :

Substitute into the equation: .

Testing :

Substitute

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