Algebra-2

According to the Rational Root Theorem, if a polynomial equation has a rational root , then 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 -4.

 

The factors of 2 are .

The factors of -4 are .

 

So the possible rational roots are .

 

Let's start testing these possible roots. Try .

Substituting into the equation:

=2 + 4 - 2 - 4

=6 - 2 - 4

=4 - 4

=0

So is a root.

 

Using synthetic division to divide the polynomial by

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